MIXED BED ION-EXCHANGE MODELING FOR
DIVALENT IONS IN A TERNARY SYSTEM
By
SUDHIR K. PONDUGULA
Bachelor of Technology
Andhra University
Visakhapatnam, AP, India
1992
Submitted to the Faculty of the
Graduate College of
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
MASTER OF SCIENCE
May, 1995
MIXED BED ION-EXCHANGE MODELING FOR
DIVALENT IONS IN A TERNARY SYSTEM
Thesis Approved:
Dean ofthe Graduate College
ii
PREFACE
Film controlled mixed bed simulations for divalent ions in a ternary system were
studied in this work. The presence of divalent ions influences the electric field produced
as a result of difference in ionic mobilities of the ions. Flux expressions, particle rates,
and column material balances are combined and appropriate numerical methods applied
to analyze the column effluent concentrations for all the ionic impurities. The model is
tested for wide range of conditions. Mathematical modeling was complex and a
generalized theoretical model was developed with assumptions where necessary.
I wish to express my deepest appreciation to my major advisor, Dr. Gary L.
Foutch, for his guidance, inspiration, patience and invaluable helpfulness throughout my
masters program. Grateful acknowledgment is also extended to Dr. Arland H. Johannes
and Dr. Martin High for serving on the advisory committee and very helpful suggestions
arid their technical assistance.
Special gratitude and appreciation are expressed to my parents for their
encouragement, understanding, and sacrifice. Particular thanks go to Mr. Vikram
Chowdiah for his help and suggestions throughout my study.
Financial assistance from school of Chemical Engineering at Oklahoma State
University, and Pennsylvania Power & Light (PP&L) for the completion of this study, are
gratefully appreciated.
I would like to express special thanks to all my friends for their encouragement in
completing this manuscript.
111
TABLE OF CONTENTS
Chapter Page
I. INTRODUCTION .
Ion Exchange Resin.................................................................................. ...,
Removal of Sulfate by Ion Exchange....................................................... '1
Objective.................................................................................................. 4
II. LITERA.TURE REVIEW.................................................................................. 6
Ion Exchange Capacity............................................................................. 6
Equilibria and Selectivity......................................................................... 6
Kinetics and Mechanism of Ion Exchange............................................... 14
III. MIXED BED ION EXCHANGE MODELING FOR
DIVALENT SPECIES-EFFECT OF SYSTEM PARAMETERS..................... 15
Abstract.................................................................................................... 15
Introduction...................... 15
Diffusion Coefficients....................... 17
Model Development................................................................................ 18
Flux Expression.............................................................................. 19
Interfacial Concentration................................................................ 20
Model Assumptions... 22
Temperature Effects................................................................................. 23
Results and Discussion............................................................................. 23
Desulphonation of Strongly Acidic Cation... 29
Flow Rate Effects...................................................................................... 33
Reduced Anion Mass Transfer Coefficients Effects................................. 38
Effects of Particle Sizes............................................................................ 41
Effects of Resin Ratios.. 47
Conclusions and Recommendations......................................................... 47
IV. EFFECT OF PLANT OPERA.TING PRINCIPLES-RESIN
HEEL AND BED CLEANING............................................................ 52
Abstract................................................................................................... 52
Introduction.......................................................................... 52
Modeling................................................................................................. 53
Comparison to Plant Experience............................................................. 54
Bed Cleaning Effects................................................................................ 60
iv
Chapter Page
LITERATURE CITED................................................................................................. 65
APPENDIX A -ANION FLUX EXPRESSIONS....................................................... 70
APPENDIX B -PARTICLE RATES......................................................................... 79
APPENDIX C -COLUMN MATERIAL BALANCES.............................................. 83
APPENDIX D -NUMERICAL METHODS.............................................................. 88
APPENDIX E -INLET CONDITIONS AND MODEL
PARAMETER VALUES............................................................... 91
APPENDIX F -COMPUTER CODE..................................... 94
v
Table
LIST OF TABLES
Page
11-1 Equilibrium Constants Determined from Binary Experimental data 10
11-2. Triangle Rule for Equilibrium Constants............................................................ 11
11-3. Estimates of Equilibrium Constants for Binary Systems at 298 0 K 13
III-I. Conductance as a Function of Temperature........................................... 18
111-2. Model Assumptions......................................................................................... 22
111-3 Temperature Effects on Sodium Exchange Parameters
Using MBIE Divalent Model......................................................................... 24
111-4. Temperature Effects on Calcium Exchange Parameters
Using MBIE Divalent Model 26
111-5. Temperature Effects on Chloride Exchange Parameters
Using MBIE Divalent Model. 29
111-6. Temperature Effects on Sulfate Exchange Parameters
Using MBIE Divalent Model 30
D-I. Coefficients ofBackward Differentiation Formulas 90
E-l. Values Adjusted for Electroneutrality Criteria 92
vi
LIST OF FIGURES
Figure Page
1. Effect of Temperature on Sodium Concentration profile for a Mixed bed
(Cation/Anion ration of 1.0) Simulation.. 25
2. Effect of Temperature 011 Calcium Concentration Profile for a Mixed-Bed
(Cation/A11ion Ratio of 1.0) Simulation............................................................. 27
3. Effect of Ten1perature on Chloride Concentration Profile for a Mixed-Bed
(Cation!A11ion Ratio of 1.0) SilTIulation............................................................. 28
4. Effect of Temperature on Sulfate Concentration profile for a Mixed-Bed
(Cation/Anion Ratio of 1.0) Simulation............................................................. 31
5. Reaction Kinetic Constant for Desulphonation of strongly Acidic Cation Ion
Exchange Resin................................................................................................... 32
6. Effect of Flow rate on Sodiun1 Concentration profile for a Mixed-Bed
(Cation/Anion Ratio of 1.0) Simulation............................................................. 34
7. Effect of Flow rate on Calciun1 Concentration profile for a Mixed-Bed
(Cation/Anion Ratio of 1.0) Simulation............................................................. 35
8. Effect of Flow rate on Chloride concentration profile for a Mixed-Bed
(Cation/Anion Ratio of 1.0) Simulation............................................................. 36
9. Effect of Flow rate on Sulfate concentration profile for a Mixed-Bed
(Cation/A11io11 Ratio of 1.0) Simulation............................................................. 37
10. Effect of Reduced Anion tv1ass Transfer Coefficient on Chloride with
System Parameters at Base Case..................................................................... 39
11. Effect of Reduced Anion Mass Transfer Coefficient on Sulfate with
System Parameters at Base Case..................................................................... 40
vii
Figure Page
12. Effect of Resin Particle Size on Sodium Concentration Profile for a Mixed Bed
SilTIulatio11........................................ 43
13. Effect of Resin Particle Size on Calcium Concentration Profile for a Mixed Bed
Simulation. 44
14. Effect of Resin Particle Size on Cilloride Concentration Profile for a Mixed Bed
Simulation 45
15. Effect of Resin Particle Size on Sulfate Concentration Profile for a Mixed Bed
SiITIulatio11 46
16. Effect of Resin Fraction on Sodium Concentration Profile for a Mixed Bed
Simulation 48
17. Effect of Resin Fractioll 011 Cilloride Concentration Profile.for a Mixed Bed
Simulation 49
18. Effect of Resin Fraction on Sulfate Concentration Profile for a Mixed Bed
Simulation 50
19. Effect of Resill I-Ieels 011 Sodium Concentration Profile using MBIE Model for
Divalent Ions 55
20. Effect of Resill Heels all Calcium COllcentration Profile using MBIE Model for
Divalent lOllS 56
21. Effect of Resin Heels on Cilloride Concentration Profile using MBIE Model for
Divale11t lOllS 57
22. Effect of Resin Heels all Sulfate Concentration Profile using MBIE Model for
Divalent Ions 58
23. Effect of Bed Cleaning every three weeks on Sodium COllcentration Profile using
MBIE model for Divalent Ions 61
24. Effect of Bed Cleaning every three vveeks on Calcium Concentration Profile using
MBIE model for Divalent Ions 62
25. Effect of Bed Cleanillg every tllree weeks on Chloride Concentration Profile
using MBIE nl0del for Divalent Ions 63
viii
Figure Page
26. Effect of Bed Cleal1ing every three weeks on Sulfate Concentration Profile using
MBIE 1110del for Divalel1t Ions 64
ix
CHAPTER I
INTRODUCTION
Ion exchange has found widespread application in the power and electronic
industries. Ion exchange is defined as a reversible exchange of ions between a solid and a
liquid in which there is no substantial change in the structure of the solid. Several
applications of ion exchange include
• Removal of objectionable cations and anions from drinking and boiler feed water.
• Production of de-ionized water.
• Treatment of trade effluents, both for the purification of liquors and for economic
recovery of small amounts of inorganic and organic substances.
• Purification of organic and inorganic chemicals.
• Treatment in analytical chemistry.
• Separation of ion mixtures.
• Others such as determination of the properties of substances in solution
for the measurement of the stability of complex ions, medical uses such as in
ulcer treatment for neutralization of excess acids by anion exchange resins and
sodium removal from the body.
The fundamental principles of ion exchange are based on a few simple facts
about the exchange reactions:
1. Ion exchange reactions are stoichiometric.
2. Ions differ in their preference to react with ion exchanging solids. The
selectivity is a measurement of the relative preference of one ion to
another for a particular material.
3. Ion exchanging materials have the ability to exclude coions. This is
known as Donnan exclusion.
4. Very large ions or polymers are subject to a screening effect and are not
adsorbed to an appreciable extent.
5. Differences in migration rates of adsorbers substances down a columnprimarily
a reflection of differences in affinity.
6. Ionic mobility are restricted to the exchangeable ions and counter ions
only.
7. Miscellaneous effects include swelling, surface area., and other
mechanical properties. These effects may involve basic chemistry of ion
exchanger and does have an influence on the overall ion exchange
kinetics.
Ion Exchange Resins
The most common ion-exchange resins are synthetic organic resins; actually a
special type of polyelectrolytes. Cross-linked polyelectrolytes can be visualized as an
elastic three dimensional hydrocarbon network to which a large number of ion active
groups are attached. The most useful hydrocarbon is the copolymerization of styrene
and divinylbenzene. This structure gives a maximum resistance to oxidation, reduction,
mechanical wear and breakage, and is insoluble in common solvents. The ion active
group is always fixed to the high molecular weight polymer and is immobile. The
electrical charge of the ion active groups is balanced by oppositely charged ions which
are mobile and can exchange with other ions of a similar charge. The chemical behavior
of ion-exchange resins is divided into two major classes.
1. Cation resins, which exchange cations or positively charged ions.
2. Anion resins, which exchange anions or negatively charged ions.
2
Sulphonation of the copolymer with sulfuric acid yields a strong cation resin
while amination yields anion resin.
Ion exchange resins are employed to promote reactions which can be catalyzed by
conventional acids and bases. Some advanta~. ~s of solid, substantially insoluble ion-exchange
catalysts are; reduction of cost because the catalyst may be used repeatedly and
usually without regeneration; increased product yield and efficiency; and elimination of
corrosion problems.
Resin properties such as capacity, equivalency of exchange, selectivity, particle
size, and crosslinkage effect the exchange kinetics. Other properties which have direct
influence on exchange performance in water Purification are (PP&L literature)
1. Surface area per unit volume, which affects kinetics,
2. Terminal settling velocities, which affect the tendency of resins to separate,
3. Bed pressure drop, which affects pumping costs and the bed's capacity to filter
insolubles,
4. BackwashlBed expansion, which affects the ability to clean resins of insoluble
materials,
5. Particle distribution, which affects all the above.
Removal of Sulfate by Ion Exchange
Impurities such as chloride and particularly sulfate in the feed water of boiling
water reactors (BWR's) represent the major corrodents in nuclear power plants.
Predicting the sulfate levels in the effluent streams requires thorough understanding of the
kinetics of divalent exchange. Sulfate occurs in BWR in two ways, as a contaminant in
water to system and from materials used in the plant. A primary mechanism is by
thermal degradation of cation exchange sites in the polished condensate (desulphonation).
Some indications point to the release of organic sulphonates from the cation resin and
4
release of sulfur species from the vessel liner. While studies are made on the
decomposition of cation resin (desulphonation) (PP&L literature) not much information
is available on the other two sources of sulfate generation. Other possible sulfate sources
are (PP&L literature)
1. Resin leakage from condensate polishers,
2. Condenser leakage with poor anion kinetics,
3. Sulfur containing organics that are not removed by the condensate demineralizers,
4. Resin leakage from reactor water clean up units (RWCU), and
5. Sulfate release from condensate polisher liner.
Sulfate exchange kinetics and equilibria in a ternary system has been studied by
Smith and Woodburn (1977). Haas (1987) supplemented it with the concept of ternary
interactions. However, little attention is paid to the development of a theoretically based
multicomponent multivalent mixed bed ion exchange model that can handle a wide range
of operating conditions.
Objective
Impurities causing intergranular stress corrosion cracking in nuclear power plants
can be minimized with the help of ion exchange. Multivalent ions such as sulfate are a
common source for corrosion along the grain boundaries on the walls of the units. Other
divalents, such as calcium, are likely to be present in condensate (particularly at freshwater
plants), and these can form insoluble deposits on nuclear fuel, resulting in local
overheating and corrosion of the fuel cladding. The main objective of this thesis is to
develop a theoretically based film diffusion controlled mixed bed ion exchange (MBIE)
model which can handle divalent species in a ternary system.
The effect of such plant operating conditions on the overall ionic impurity levels
expected, are discussed in the following chapters. Actual plant input is supplied by
Pennsylvania Power & Light. The results are analyzed and compared with plant
experience.
5
CHAPTER II
LITERATURE REVIEW
An extensive literature review of ion exchange applied to ultrapure water
processing has been carried out by Haub (1984), Yoon (1990), Zecchini (1990) and, more
recently, by Lou (1993). This review concentrates on the objectives of this thesis.
Ion exchange capacity
Practically, ion exchange processes are considered as pseudo-chemical reactions
which require the initial concentrations of exchanging species to be expressed in both
phases. Data for the liquid phase are easily obtained, but the corresponding data for the
resin phase requires a knowledge of the ion-exchange capacity, which is defined as the
number of equivalents of exchangeable ions per unit weight or volume of the resin. The
weight or volume ofthe resin refers to a particular ionic form and is usually the hydrogen
form for a cation resin and chloride for an anion resin (Grimshaw and Harland, 1975).
For the case of weak acid, weak base, and polyfunctional resins, the maximum degree of
exchange depends upon the pH of the liquid phase.
Equilibria and selectivity
One of the controlling factors governing the use of ion-exchange separations is
the equilibrium distribution of ions between the resin and solution phases. When an ion
exchanger or resin bead is placed in an electrolyte solution, equilibrium will be obtained
6
7
after a certain time. At this point, the ion exchanger and solution both contains the
exchanging ions. However, the concentration ratio of the two ions will not be the same in
both phases. The preference for one ion over another by the exchanger is known as
selectivity. Selectivity depends on the nature of the counterions, the nature of the fixed
charges in the matrix, the degree of ion exchanger saturation, the total solution
concentration, and the external forces such as temperature and pressure. The ion
exchanger prefers counterions that have the higher valence, smaller equivalent volume,
greater polarity, and stronger association with fixed ionic groups in the matrix
(Helfferich, 1962).
The following observations serve as a guide in predicting and planning ionexchange
systems (Kunin, 1960).
1) At low concentrations and ordinary temperatures, the selectivity
increases with increasing valency ofthe exchanging species:
Na+ <Ca+2 < AI+3 <Th+4
2) At low concentrations, ordinary temperatures, and constant valence, the
selectivity increases with increasing atomic number of the
exchanging species:
Li <Na < K < Rb < Cs; Mg < Ca < Sr < Ba
3) Organic ions of high molecular weight and complex metallic anionic
complexes exhibit high exchange capacity.
4) Ions with higher activity coefficients have greater exchange capacities.
The stoichiometric exchange between the counterions A in the resin phase and B
in the solution phase may be written as
ZB(A)ZA + ZA(B)ZB<=:> ZA(B)ZB + ZB(A)zA
where
ZB(A)zA, ZA (B)ZB = concentrations in resin phase
Z = valence
8
The selectivity is usually defined in terms of the selectivity coefficient (K~), which is the
mass action relationship written for the reaction according to a particular choice of
concentration units:
(XB)ZA(XA)ZS
(XA)ZS(Xn)zA
where
m = molal
C = molar
x = equivalent ionic fraction
When the exchanging species are all univalent, all three coefficients have the same
numerical value i.e.
KB =KC
B =KX
B
rnA A A
A more widely used coefficient in physical chemistry is the distribution
coefficient. When any two solutes are contacted by mechanical shaking for several hours
with an equal amount of resin and solution, then by comparing the concentration of solute
left in the solution with the concentration before exchange, distribution coefficient may
be calculated by
Kd= Ms .(volumes of solutions)/(mass of resins)
ML
where
Ms and ML are the fraction of the cation M in the resin and liquid phase respectively
and Kd is the distribution coefficient at equilibrium. The ratio of the distribution
coefficient of solute A to that ofB is defined as the separation factor.
9
In general, all practical and important ion-exchange processes deal with more than
two exchangeable ions. However, most of our knowledge of the behavior of ionexchange
comes from the study of binary systems. Few systematic studies have been
done on multicomponent ion exchange because of the complexity of both experimental
and theoretical multi-ionic systems.
Prediction of multicomponent ion-exchange equilibrium is needed for the design
of exchangers which operate over a wide range of conditions. A theoretical model which
allows the equilibrium behavior of multicomponent systems to be predicted would,
therefore, be extremely useful. However, little attention has been paid to the influence of
resin composition on the affinity of ions in a multi-ionic resin.
de Lucas et al. (1992) studied t~e cation-exchange equilibria between Amberlite
IR-120 resin and aqueous solution of calcium, magnesium, potassium, and sodium
chlorides and hydrochloric acid. Experimental data for ion-exchange equilibria of the
ternary and quaternary systems are reported in this study. They also developed a model
which allows the prediction of multicomponent ion-exchange equilibria from binary data.
They concluded that the predictions of ternary and quaternary systems based solely on
the binary data are in good agreement with the experimental results. According to this
study, methods for the prediction of multicomponent ion-exchange equilibria are
classified into four main groups.
• Models assuming ideality of the exchange equilibria (i.e., ideal solutions with
negligible effect due to resin swelling and hydration) with a constant separation
factor and activity coefficients of all components in the solid phase equal to unity.
• Models assuming regular systems with a linear transformation between the
separation factor and the composition in the solid phase.
• Treating ion exchange as a phase equilibrium using standard procedures
developed for solution thermodynamics. Surface effects are taken into account
10
by introducing surface excess variables similar to those used to study adsorption
from liquid mixtures on solids.
• Theoretical Models which consider non ideal or real systems, so they should be
more accurate in predicting equilibrium behavior.
Among the different models, a model based on the mass action law is applied in
this study.
Table 11-1 shows the equilibrium-constants determined from experimental data.
Table 11-2 shows the triangle rule for ternary system.
Table 11-1
Equilibrium constants determined from binary experimental data (de Lucas et aI., 1992).
AlB KB T(K) E(~ A
H+/Na+ 1.760 283
1.674 303 7.3
1.510 323
H+/Ca2+ 25.70 283
29.04 303 6.2
31.32 323
Na+/Ca2+ 9.121 283
10.86 303 2.6
12.20 323
11
Table 11-2
Triangle rule for Equilibrium Constants (de Lucas et al.., 1992).
System
KCa KNa2 KH Na' H • Ca- 1
283 K
1.1
303 K
1.05
323 K
0.89
Triayand Rundberg (1987) considered the selectivity coefficient distributions by
deconvolution of ion exchange isotherms. The ion exchange isotherm is the equilibrium
solid-phase concentration of a given ion as a function of the aqueous-phase concentration
when the temperature and ionic strength are held constant. The solid-phase concentration
increases with aqueous-phase concentration until the exchangeable sites are saturated.,
provided the structure of the ion exchanger does not change as the adsorbed ions are
replaced. The point of saturation (i.e.,exhaustion of resin sites) is determined by the ion
exchange capacity.
de Bokx et al. (1989) studied the ion-exchange equilibria of alkali-metal and
alkaline-earth-metal ions by using surface-sulfonated polystyrene-divinylbenzene resins.
This study employs a chromatographic method in which one of the exchanging ions is
present in trace quantities only. It was found that the equilibrium coefficient is
independent of the concentration of the liquid phase, and therefore specificity in ion
exchange is due solely to interactions in the resin phase. The data could be interpreted by
enthalpy-entropy compensation. Equations were derived that relate the equilibrium
coefficient to a product of the difference between two interaction parameters and a factor
that is constant within a class of ions. It was shown that selectivity is determined by the
interaction between adsorbed ions and not by the interaction of separate adsorbed ions
with the resin.
12
Horst et al. (1990) believe systems in which equilibria is based on separation
factors or equilibrium constants have to be closer to ideal and the predictions aren't good
otherwise. This led to study of ion exchange equilibria on weak acid resins by a
theoretical approach in which fixed sites and counterions are assumed to form surface
complexes. The electric charges of the fixed sites generate an electric field normal to the
resin surface. Counterions are located in individual sorption layers which have a certain
charge density. Due to the existence of one layer for each kind of counterions, the entire
resin phase can be considered as a series of electric capacitors. For the exchange of
protons with metal counterions, a set of two characteristic quantities are derived [rOITI
experiments. By means of this set of quantities, the equilibrium is calculated for a broad
range of initial conditions. They applie4 the relationships of a series of electric capacitors
and predicted the multicomponent equilibria using the sets of binary exchange
parameters. The assumption that all counterions are located in their characteristic layers
led to a simplified mathematical method. This method provided an excellent agreement
between experimental and predicted equilibria.
Smith and Woodburn (1978) developed a generalized model to predict
multicomponent ion exchange equilibria from binary data. The binary systems used in
their study are SO;- - CI-, 80;- - NO~, and CI- - NO~ on a strong base anion exchange
resin. These systems exhibit non-ideal characteristics in both phases and the
experimental characterization is based on the reaction equilibrium constants. Wilson's
correlation's for the activity coefficients are used in the model. Table 11-3 shows the
values of equilibrium constants.
13
Table 11-3
Estimates of equilibrium constants for binary systems at 298 oK (Smith et al.~ 1978).
Ion exchange reaction
R2S04 +2N03 <:::>2RN03 +S04
R2S04+2CI<=>2RCI+S04
RCI + N03 ¢:> RN03 + CI
The three equilibrium constants are related as
Equilibrium Constant
K~g~) == 72.939
K~~4 == 5.094
K~~1 == 3. 780
Helfferich (1967) gave a general analytical solution for systems with an arbitrary
number of exchanging species for conditions of local equilibrium, absent axial diffusion
and dispersion, with constant separation factors, uniform presaturation, and constant feed.
This solution is based on the coherence (stability) of chromatographic boundaries.
Tondeur and Klein (1967) presented a general analytical solution for the
simultaneous material balance and constant-separation-factor equilibrium relations
pertaining to zones of varying compositions in multicomponent, fixed-bed ion exchange
columns. They also provided algebraic and numerical methods determining the constants
occurring in the analytical solution, and obtaining the overall concentration profiles of
three and four component systems.
Clifford (1982) used a similar approach and calculated the concentration profiles
and column histories from a derived set of general rules and equations assuming constant
separation factors. He predicted nitrate and sulfate effluent breakthrough curves from
weak base anion beds with four-component feed (80;-, NO~, CI-, HCO; ) solutions using
multicomponent equilibrium theory. The theory also predicted the length of a run and the
final composition of the exhausted bed when treating nitrate-contaminated water.
14
Kinetics and Mechanism of Ion Exchange
The rate at which ion-exchange proceeds is a complex function of physicochemical
mechanisms. A high rate of exchange is generally favored by the following
conditions:
1) small particle size resin,
2) efficient resin-solution mixing,
3) high solution concentration,
4) high temperature,
6) low cross linked resin.
Kitchener (1954) evaluated ion exchange kinetics in detail. The factors
mentioned above were considered. A more simplified treatment is to adopt the Nemst
film diffusion theory. The solution is considered perfectly mixed. Transport through the
Nemst film is treated by Fick's law with a certain equivalent thickness, 8 (fixed by
hydrodynamic factors), for the hypothetical unstirred film. Diffusion inside the resin is
the last step.
Overall exchange kinetics is too complicated to analyze mathematically; but a
satisfactory method is provided by Boyd, Adamson and Myers (1947), who made use of
Nemst (1904) film theory. In film theory, the ion exchange reaction is controlled by two
simultaneous diffusion steps - diffusion through the Nemst film, and diffusion through
the resin particle. However, many applications use single diffusion processes because
either diffusion in the boundary film becomes rate-determining or diffusion through the
boundary film is so rapid that the slow step is almost entirely confined to diffusion inside
the resin bead.
Results of kinetic studies lead to values for the exchange-diffusion coefficients of
a pair of ions in either the resin phase or aqueous phase. However, independent
determinations of diffusion coefficients inside resins is possible with the help of radio
active tracers (Saldana et aI., 1953).
CHAPTER III
MIXED BED ION EXCHANGE MODELING FOR DIVALENT SPECIESEFFECT
OF SYSTEM PARAMETERS
Abstract
A model for ternary mixed bed ion exchange (i.e. six component exchange - three
cations and three anions) including divalent species is developed and tested for various
system parameters. This model is capable of handling variations in cation-to-anion resin
ratio, mass transfer coefficient, particle size, flo\v rate, and bed composition. The model
is extended to address bed cleaning every three weeks whereby average particle loading
after cleaning is used as the initial loading for the next three weeks.
Introduction
The feed water of a boiling water reactor can contain suspended and soluble
impurities. The suspended impurities are primarily metal oxides from corrosion~ erosion
and wear of system materials. They are of concern because they will tend to foul the
nuclear fuel. The soluble impurities come from the ingress of cooling water during
condenser leaks and from residual regenerants from demineralized water production.
Certain of the soluble impurities, particularly chloride and sulfate, \vill cause or accelerate
intergranular stress corrosion cracking (IGSCC) of reactor system materials present at
high enough concentration in reactor water. Industry guidelines suggest that chloride and
sulfate be maintained well below 5 ppb in reactor water. For a plant with 1% reactor
15
16
water cleanup system, this means that the feedwater must contain less than 50 ppt
chloride and sulfate. Ion exchange in the condensate polisher must be capable of
removing impurities from condensate down to these levels. Minimizing these impurities
will reduce the growth rate ofthe cracks once they are formed. The principle sources of
corrosion products in the feed water ofBWR's results from condenser leakage and resin
leachability (source of sulfate release). The condensate/feed water impurities must be
kept low to maintain reactor water purity. Nuclear power plants often experience
difficulty in meeting low impurity levels (usually 5 ppb for corrosion products). Ion
exchange is the most suitable unit operation for this purpose.
Many attempts have been made to develop general, multicomponent, ion
exchange models for non ideal behavior. Klien et ale (1987) considered only ideal
components of a ternary system. Soldatov and Bychkova (1970) described the ternary
system K+ - NH4 - H+ based on activity coefficients in the binary mixture calculated
from experimental data and applied to the ternary mixture. For accurate results, the
treatment requires that the main binary system be close to ideal.
Danes and Danes (1972) proposed a method for calculating ion exchange
equilibria ofpolyionic systems where the molar excess free mixing enthalpy of the
resinates is expressed as a polynomial. The predictive power of the method is limited to
systems which obey ideal or regular solution rules.
Basic principles of ion exchange coupled with kinetics of individual species are
applied in developing the current model. Because of the presence of divalent species,
however, some complications arise in the mathematical modeling. Assumptions and
conditions are applied at appropriate junctures where necessary.
The objective ofthis work is to develop a film controlled neutralization model for
MBIE that includes divalent species in a ternary system. The diffusion coefficients
(given in Table III-I) for the ionic species use the limiting mobilities given by Robinson
17
and Stokes (1959). Non-ionic mass transfer coefficient correlation's are applied in this
work to account for the effect of differing mobilities of the ions on the overall exchange
process. Data from Pennsylvania Power & Light (PPL) is used in the model and
computer predictions are analyzed.
Diffusion Coefficients:
In an electrolyte solution the solute is in the form of ions, either cations or anions.
The relative mobility of all ions depends on their size. However, all the ions present must
also satisfy the overall charge balance. The Nernst (1888) equation provides a simple and
accurate method for predicting diffusion coefficients in electrolyte solutions by relating
the diffusion coefficients to electrical conducti\'ities:
where
D~ =(RT /~)A.~
3-1
3-2
A~= electrolyte conductance at infinite dilution, (A / cm2
)(cm/ V)(cm3
/ g - equiv.)
T= absolute temperature, OK
Equation 3-1 is used to relate temperature to the ionic diffusion coefficients. The
Nernst equation has been verified experimentally for dilute solutions (Divekar et aI.,
1987). Temperature and equivalent conductance are correlated by least squares at infinite
dilution (given in Table III-I).
18
Table 111-1
Conductance as a Function of Temperature (Divekar et aI., 1987).
A~ =221.7134 +5.52964 T -0.014445T2
A~H =104.74113 +3.807544 T2
A~a =23.00498 +1.06416T +0.0033196 T2
A~I = 39.6493 +1.39176 T +0.0033196 T2
AOs =(35.76 + 2.079T)/2
A~a = (23.27 +1.575T)/2
3-3
3-4
3-5
3-6
3-7
3-8
Combining eq 3-1 and 3-2 - 3-7 provides expressions to relate the effect oftemperature
on the diffusion coefficients of ions of the form
Dj =(RT /F!)(Aj+BjT +CjT2
)
Model Development
3-9
The exchange of divalent species in a film controlled homogeneous MBIE is
addressed in this model. The film diffusion fluxes are described using the Nemst-Planck
equation combined with the continuity equation for the film. Basic assumptions relevant
to the model are used in developing the interfacial concentrations. Final effluent
concentrations are determined by using the column material balance combined with the
rate expressions which are solved numerically. Numerical methods were based primarily
on stability rather than computationally faster methods. These are discussed in detail in
APPENDIXD.
19
Flux Expression
Zecchini et al. (1990) discussed the ternary interactions in univalent ions.
Divalent ions affect the electroneutrality and no net current flow expressions in t11e lTIodel
development. The electric field produced as a result of difference in ionic mobilities,
changes significantly in the presence of divalent ions. This has a direct influence on the
flux expression which is needed to determine particle rates. Electroneutrality and no net
current flow criteria are used in simplifying the continuity equation for a liquid film
(no net current flow),
(electroneutrality),
controlled process.
Cn +~ + 2C1, = Cc + Co + 2Cs
I n + J h + 2J b = J c + J 0 + 2J s
I n = J h = J b = 0
J c = J o = J s = 0
(anion exchange; no coion flux),
(cation exchange; no coion flux)
Combining the above four relations and eliminating the electric potential, <1>, in the
Nemst-Planck equation for each of the ions and considering that reactions are restricted to
bulk phase neutralization (i.e., changes in flux w.r.t. radial position is negligible):
dJi = 0 yields a linear profile for coion concentration within the film of the form
dr
co -C·
C = P P r + C·
P 8 P
where
Cp =Ch +Cn +Cb
Combining this expression with Nernst-Planck equation and integrating from the bulk
phase to the film yields a final flux expression of the form
C* *
l-(-P)(~)
Co C?
-J.8=(1-Z.)D.( pI)
1 1 1 c*
P 1 1+(-)(-)
Co C?
P 1
20
This expression is used for all the individual ions to determine the effective diffusivity.
The static film model combined with the flux of the species results in
d < Cj > = K'a (C? - C~) = -l.a
dt 1 S 1 liS
resin phase fractional concentration can be written as
Y· =< C. > IQ 1 1 ,
and the liquid phase as
x·1 = C.1 ICT
Particle rates are developed by combining the flux expression and static film model.
Final particle rate for divalent ion results as
Oyj = 9R .!S..(XO
en sK - x*) S S
C
Interfacial Concentrations
Interfacial concentrations for the ions are developed using the basic principles of
ion exchange using the Nemst-Planck equation. A simultaneous solution of
electroneutrality, no net current flow, no coion flux, and Nemst-Planck equations using
the principles of film diffusion controlled process, leads to an expression for interfacial
concentration in terms of the known parameters.
A final expression eliminating the flux terms is of the form
21
This is an expression which relates the concentrations in bulk phase to the
concentrations at interface at any given time. This transfonns the above expression from
bulk phase concentrations to interfacial concentrations. Selectivity coefficients for eacll
of the species can be written as:
These expressions are used to eliminate the chloride and hydroxide interfacial
concentrations in favor of sulfate. The final equation for sulfate interfacial concentration
is of the form
where
Chloride and hydroxide interfacial concentrations are obtained using selectivity
coefficients.
22
Assumptions:
The presence of divalent species led to complex mathematical modeling.
Assumptions have been minimized to develop a generalized theoretically based divalent
model. Table 111-2 lists the assumptions that have been applied.
Table 111-2
MODEL ASSUMPTIONS
1. Film diffusion control
2. The Nernst-Planck equation incorporates all interactions among diffusing ionic
species.
3. Pseudo steady state exchange (Variations of concentration with space are much
more important than with time)
4. Local equilibrium at solid-film interface
5. No coion flux across the particle surface
6. No net coion flux within the film
7. No net current flow
8. Reactions are instantaneous when compared with the rate of exchange
9. Ternary system with divalent species exchange
10. Curvature ofthe film is negligible
11. Uniform bulk and surface compositions
12. Activity coefficients are constant and unity
13. Negligible axial dispersion
14. Isothermal, isobaric operation
15. Negligible particle diffusion resistance
16. Selectivity Coefficients are constant and temperature independent
23
The major assumption underlying this model is the film diffusion controlled process
which is most accurate for dilute solutions «5 ppb). Selectivity coefficients are assumed
constant and independent temperature. Electroneutrality criteria for the inlet
concentrations is fixed by adjusting the pH.
Temperature Effects
An MBIE model for divalent species has been developed and tested for
temperature effects on equilibria and kinetics of ion exchange. Divekar et al. (1987)
modified the model developed by Haub and Foutch (1986) to account for temperature
effects for univalent species. The curr~nt model for divalent exchange was tested for
temperatures ranging from 32.2 to 600 c·
Expressions for the temperature dependent terms (ionic diffusion coefficients,
ionization constant for water, bulk solution viscosity) were obtained from the literature.
Variations in temperature affects many system parameters like solution viscosity, ionic
diffusion coefficients, selectivity coefficients, and ionization constant of water. This
model calculates all of these temperature dependent parameters except selectivity
coefficients which were not available in the literature for the desired species.
Results and Discussion
The effect oftemperature on concentration profiles were tested at 32.2, 48.9, and
600 C. This was done for a cation to anion ratio of 1:1 by volume, and a flow rate of
42.7 gpm/ft2. All other conditions were at the base case (Appendix E). Diffusion
coefficient, mass transfer coefficient, and solution viscosity were calculated as a function
of temperature. The effect of increase in temperature from 32.20 C to 600 C increases the
ionization constant of water from 1.8E-14 to 10E-14 (Le., both hydrogen and hydroxyl
24
ion concentrations increase in the bulk phase. Divekar et aI, 1986). This results in a
reduced concentration gradient for the mass transfer of the hydrogen and hydroxyl ions
and consequently poor overall rate exchange is observed at higher temperatures.
Sodium: Table 111-3 shows the calculated values for sodium, at the different
temperatures considered. A decrease in temperature from the base case (at 600 C) to
32.20 C, causes the effluent equilibrium leakage of sodium concentration to decrease by
45.8%. As shown in Figure 1, the breakthrough curves are steeper at higher
temperatures. Breakthrough occurs 200 days earlier for sodium when the process is
operated at 600 C compared to 32.20 C.
Table 111-3
Temperature Effects on Sodium Exchange parameters Using
MBIE Divalent Model.
Temperature Diffusion Mass Transfer Effluent % Change of Effluent
oC Coefficient Coefficient Leakage Leakage from value at
(cm2/s) (cm/s) Values (Ppb) 600 C
32.2 0.165E-4 0.023 0.026 -45.8
48.9 0.238E-4 0.031 0.035 -27.1
60.0 0.294E-4 0.037 0.048
32.2 C
I
I
#.
I
I
I
I
~
I
,
~
I
#.
I
~
~
~
~
, ~
~
~
~
400 600 800 1000 1200 1400 1600 1800
Time (Days)
Figure 1. Effect of Temperature on Sodium Concentration Profile for a Mixed-Bed
(Cation!Anion Ratio of 1.0) Simulation
l0
V.
26
Calcium: Table 111-4 shows the calculated values for calcium, at the three temperatures
considered. A decrease in temperature from base case (at 600 C) to 32.20 C, causes the
effluent equilibrium leakage of calcium to decrease by 76%. As shown in Figure 2, the
breakthrough curve is steeper when the process is run at 32.20 C.
Table 111-4
Temperature Effects on Calcium Exchange Parameters using
MBIE Divalent model.
Temperature Diffusion Mass transfer Effluent % Change of
°C Coefficients Coefficient Leakage Effluent Leakage
(cm2/s) (cm/s) Values (Ppb) from value at 600 C
32.2 0.100E-4 0.1671£-1 0.841E-8 -76.0
48.9 0.144E-4 0.2247E-1 0.186E-7 -46.7
60.0 0.175E-4 0.2660£-1 0.349E-7
Chloride: Table 111-5 shows the calculated values for chloride, at the three temperatures
considered above. A decrease in temperature from base case (at 600 C) to 32.20 C,
causes the effluent equilibrium leakage of chloride to decrease by 57.7%. As shown in
Figure 3, the breakthrough curves of chloride are more steeper compared to sodium.
Breakthrough occurs 100 days earlier when the system is run at 600 C compared to
32.20 C.
1.00E-06
1.00E-05 -
1.00E-03
~ 1.00E-04
C.
C.
'--'" ....o=...... ..=...... =~
CJ
o==
U ~
..... "
== ~=e~
1.00E-07 -
1.00E-08
1.00E-09
o 200 400 600 800 1000 1200 1400 1600 1800
Time (Days)
Figure 2. Effect of Temperature on Calcium Concentration profile for a Mixed-Bed
(Cation!Anion Ratio of 1.0) Simulation
I,J
-.J
1.00E+01 i I
~ '- ----- - -- 49C.' / 32.2 C ,, I
, /
",
,'I
,'/
•'/
,'/
'/ I
_.. - -- -- -_. -_ ... _.""'/
--------"""
~.c
cc.. 1.00E+00
~..,=o...... .=......
=~ 1.00E-01-
CJ
== oU
.... =~
~ 1.OOE-02 1 _
~
~
200 400 600 800 1000 1200 1400 1600 1800
1.00E-03 , r
o
Time (Days)
Figure 3. Effect of Temperature on Chloride Concentration profile for a Mixed-Bed
(Cation!Anion Ratio of 1.0) Simulation
t.J
00
29
Table 111-5
Temperature Effects on Chloride Exchange Using
MBIE Divalent Model.
Temperature
oC
32.2
48.9
60.0
Diffusion Mass Transfer Effluent % Change of Effluent
Coefficients Coefficient Leakage Values Leakage from value at
cm2/s (cmls) (Ppb) Base Case (600 C)
0.239E-4 0.343E-1 0.358E-2 -57.7
0.332E-4 0.453E-1 0.619E-2 -27.0
0.402E-4 0.534E-1 0.848E-2
Sulfate: The main sources of sulfate in the reactor units of industries are due to
a) Desulphonation of the cation resin (release of sulfate),
b) Release of organic sulfonates from the cation resin, and
c) Release of sulfur species from the vessel liner.
The model addresses the desulphonation effect.
Desulphonation of strongly acidic cation ion exchange resin (release of sulfate):
The decomposition of cation resin has been studied by several investigators (Fisher 1993,
Fejes 1969, Marinsky and Potter 1953). Most of the data available has been developed at
temperatures much higher than that employed in power plant condensate polishing. The
rate constant for desulphonation versus liT for several of these studies is available in the
literature (Fisher 1993). A least squares method is employed to obtain the rate constant
as a function of temperature.
K = 7.5e + 6EXP(-10278.6/ (T + 273.16)) (3-10)
30
where
K is a first order rate constant in hr-1
T is in 0 C.
Sulfate throw is assumed constant from each slice. The whole bed is considered as a
finite set of slices. For the base case at 600 C, desulphonation increases the effluent
sulfate concentration by five orders of magnitude (10-7 ppb to 10-2 ppb). As shown in
Figure 4, the effect oftemperature has the greatest effect on sulfate. A decrease of
temperature from base case (at 600 C) to 32.20 C, causes effluent equilibrium leakage
sulfate concentration to decrease by 90.5%. Breakthrough for sulfate did not occur for
both the higher temperatures for the current column conditions. At a temperature of
32.20 C, a steep increase in the curve is observed after twelve hundred days. Table 111-6
shows calculated values in sulfate for the three temperatures considered above. Figure 5
shows the plot of rate constant for desulphonation versus Iff.
Table 111-6
Temperature Effects on Sulfate Exchange Parameters Using
MBIE Divalent Model.
Temperature Diffusion Mass Transfer Effluent % Change of
oC Coefficients Coefficient Leakage Effluent Leakage
(cm2
/ s) (cm/s) Values (Ppb) from 600 C
32.2 0.I40E-4 0.240E-l 0.343E-3 -90.5
48.9 0.197E-4 0.320E-l 0.147E-2 -59.4
60.0 0.238E-4 0.377E-l 0.362E-2
1.00E-01 --
1.00E-02
1.00E-03
49C
, .
~
,•
•
•
•
,,
•
•
•• ,
,,
,
32.2 C •
• I ,
• • .. til
60C
"' .
Ii-------
1.00E+01
~.c 1.00E+OOC.
C.
'-"'" ..o=.-.
=.. ..... =~
CJ =o
U... =~=e~
1.00E-04 I r
o 200 400 600 800 1000 1200 1400 1600 1800
Time (days)
Figure 4. Effect of Temperature on Sulfate Concentration profile for a Mixed-Bed
(Cation!Anion Ratio of 1.0) Simulation
v.>
~
-........................... ~
•
~ Sallie Fisher's Data (1987, PP&L Internal Report)
I
J.
.c
If)
I~
~
~=C':
~
~=o
U
~
~
C':
~
10000.000 I
• 1000.000 I •
100.000
10.000
1.000
0.100
0.010 ---I T --- --1-- -----
•
--, r----
-.,
T r
I
r
0.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003
liT ('K)
Figure 5. Reaction Kinetic Constant for Desulphonation of strongly Acidic Cation
Ion I~xchange Resin.
'.jJ
IJ
Flow Rate Effects
Figures 6 through 9, show the effect of change in flow rate on predicted effluent profiles.
The flow rates used were 42, 50 and 57 gpm/ft2
• All simulations \vere conducted at
60°C (base case).
Sodium: Figure 6 shows that effluent equilibrium leakage values are not affected by
varying the flow rate. Sharp curves and early breakthrough occurs for higher flow rates.
By increasing the flow rate from 42 gpm/ft2 (base case) to 57 gpm/ft2
, breakthrough
occurs earlier by 200 days. By operating with a higher flow rate of 57 gpm/ft2
, the bed
is saturated approximately 200 days earlier than that observed for base case.
Calcium: Calcium exhibits a trend similar to sodium but the effluent concentrations are
much less. Figure 7 shows equilibrium leakage values do not get affected by variation in
flow rates. By increasing the flow rate from 42 gpm/ft2 (base case) to 57 gpm/ft2
,
breakthrough occurs earlier by 180 days. The curves get steeper at higher flow rates.
Chloride: Figure 8 shows the predicted effluent equlibrium leakage of chloride. A trend
similar to sodium curve is seen in the case of chloride. Equilibrium leakage values for all
three cases are the same. Breakthrough is characterized by steep curves in all three cases.
For a flow rate of 57 gpm/ft2
, breakthrough is approximately 180 days earlier compared
to the base condition at 42 gpm/ft2
•
Sulfate: Unlike sodium, calcium and chloride, sulfate effluent leakage values shows a
strong function of the flow rate. Higher flow rates decrease the effluent leakage values.
A 13.4% decrease in effluent leakage value is observed when the flow rate is increased
from 42 gpm/ft2 (base case) to 57 gpm/ft2
• The Primary reason for this behavior is seen
6.00E-01
~
~
eo.
'-"
c
..o. ~
~
I- ..C
OJ
~
Co
U
......
C
aJ = 5
~
5.00E-01
4.00E-01
3.00E-01
2.00E-01
1.00E-01
57 gal/min I I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
50 gal/,min
100 200 300 400 500 600 700 800 900 1000
O.OOE+OO , ,
o
Time (days)
Figure 6. Eflect of Flow rate 011 Sodiulll Concentration profile for a Mixed-Bed
(Cation/Anioil Ratio of 1.0) Sinlulation
v,)
~
6.00E-08 •
~ 5.50E-08
57 gal/min • I 5~g~/min
.c
, I
c..
I
~
c..
• I
"-"" =
•
0 5.00E-08
I I I 42 gal/min ... ......
I I
e':
l-
I
~=
• I
aJ 4.50E-08
•
<:J =
I I
0
•
U
• J
...... 4.00E-08 =
I
aJ
. I
= I
E
I I
~ 3.50E-08
. ~ /
- - - .... -~ .... .".,
3.00E-08
o 100 200 300 400 500 600 700 800 900 1000
Time (days)
Figure 7. Effect of Flo\\T rate on Calciunl Concentration profile for a Mixed-Bed
(Cation/Anion Ratio of 1.0) Sinlulatioll
v.,)
Vl
1.00E+01
I
42 gal/mi1t_ .
~
- I
~
- ,
c. 50 gal/lniQ
• /----
C. 1.00E+OO
--
"'-"'"
,
-- -.
=
, .' 0 57 gal/min
I ..... ~
, I e':
l-
.
~
- ~. I =~ 1.00E-01
,
u I = •
0 •
U
, I
~
,
= I
~
I
= 1.OOE-02
,
/ e .
~
1.00E-03
o 100 200 300 400 500
Time (Days)
600 700 800 900 1000
, Figure 8. EHect of Flow rate on Chloride concentration profile for a Mixed-Bed
(Cation/l\nion l~atio of 1.0) Sinlulation
!...#,J
0\
3.50E-03
3.40E-03
~-----------
3.70E-03
~ 3.60E-03 ..c
c.
c.
~=o
......
~
~
J.
~=aJ
~
Co
U-= 3.30E-03
aJ =E~
3.20E-03
3.10E-03
~ . . .
I
42 gal/min
50 gal/min
57 gal/min , ,
-I
".
".. ~
I
o 100 200 300 400 500
Time (Days)
600 700 800 900 1000
Figure 9. Effect of Flow rate on Sulfate concentration profile for a Mixed-Bed
(Cation/Anion I~atio of 1.0) Simulation
VJ
-......J
38
in the generation term for sulfate which is a function of flow rate. Small 'peaks' of the
order of 0.3E-3 ppb are observed in the concentration profiles. This interval corresponds
to chloride breakthrough. This could be attributed to numerical instability.
Reduced Anion Mass Transfer Coefficient Effects
The mass transfer coefficients of chloride and sulfate are reduced by half to note
the changes in the concentration profile values at base case conditions. Mass transfer
coefficients of sodium and calcium are not changed. All the other system parameters are
maintained at the base condition.
Chloride: Figure 10 shows that equilibrium leakage effluent concentrations are not
affected by reducing the mass transfer coefficient by half. Higher mass transfer
coefficients exhibit sharper breakthrough curves as shown in the figure. Reducing the
mass transfer coefficient by half caused an earlier breakthrough by approximately 100
days. Higher mass transfer coefficients exhibit sharp curves.
Sulfate: Unlike chloride, the equilibrium leakage effluent concentrations of sulfate
showed a 100 % (0.36E-2 ppb to 0.72E-2 ppb) increase by reducing the sulfate mass
transfer coefficient by half. Breakthrough didn't occur in both the cases. The leakage
values were fairly constant throughout the operation in both the cases. One reason for the
sudden increase in effluent concentrations is associated with the desulphonation effect.
The sulfate throw from each slice is assumed constant and the expression given as:
1.00E+01
,..-.....
.t:J c..
C. 1.00E+OO
~=o
... .....
~
.J... C
QJ 1.00E-01
u=o
U
..... =~=e~
1.00E-02
1.00E-03
~
/
I
/
/
Reduced Anion Mass Transfer Coefficient /
I
/
.".;
Coefficient
o 100 200 300 400 500
Time (days)
600 700 800 900 1000
Figure 10. Effect of Reduced Anion rvlass Transfer Coefficiel1t on Cilloride witll Sys~em ·
Paranleters at Base Case
vJ
\0
8.00E-03
...... =~= ~ 2.00E-03
C+-C
~
,..-...
~c.
c.
'"-"" .=o- ......
~
..I..-.. =aJ
CJ =o
U
7.00E-03
B.OOE-03
5.00E-03
4.00E-03
3.00E-03
~ - - - - - - - - - -- - - _.
Reduced Anion Mass Transfer Coefficient
Base Case Mass Transfer Coefficient
1.00E-03
O.OOE+OO
o 100 200 300 400 500
Time (Days)
BOO 700 800 900 1000
Figure 11. Effect of Reduced Anion Mass Transfer Coefficient on Sulfate with System
Paranleters at Base Case
~o
DS =(7 .5e +6EXP(-10278.6/ (T(OC) +273.16))
xHTx 3.1415(D2
) x qc)(vsx d pa ) x FeR
/(NT x 3600 x FR x KLC x (1- VD))
where
DS= desulphonation (meq/ml)
HT = height of the column in cm
D = diameter of the column in cm
VS = superficial velocity through the bed
dpa = anion particle diameter in cm
FCR = fraction of cation resin in the bed
NT = number of distances steps along the column
FR = flow rate in cm3Is
KLC = chloride mass transfer coefficient
41
(3-11 )
VD = bed void fraction
DS (eq. 3-11) is the desulphonation transformed into consistent units to be used in the
computer code. Reduction in the mass transfer coefficient of chloride has an inverse
effect on the desulphonation. This increased uniform desulphonation throughout the bed
causes higher leaching and consequently higher effluent leakage sulfate concentrations
are observed.
Effects of Particle sizes
The effects of resin particle size on the predicted effluent concentrations were
tested for the following two categories.
a) Cation particle = 0.8 cm; Anion Particle = 0.6 cm
b) Cation Particle = 0.65 cm; Anion Particle = 0.55 cm
All the other parameters are at base case.
42
Figure 12 shows that equilibrium effluent leakage sodium concentrations are not
affected by change in particle size. The bed saturation time is the same in both cases.
Mass transfer coefficients effect the breakthrough curves. Higer mass transfer
coefficients give sharper breakthrough curves. Mass transfer coefficients are calculated
using Kataoka and Carberry correlations and are related to particle size as:
Kia(d p
)-O.5 for Re ~ 20, and
Kia(dp )-2/3 for Re ~ 20
Also, the sodium rate expression is proportional to the ratio of anion to cation partcle
SIze.
Figure 13 shows the effluent calcium leakage concentrations. A similar trend to
sodium is observed.
Figure 14 shows the effluent leakage chloride concentrations. Chloride is taken as
the reference ion in the divalent model and consequently the chloride rate expression is
independent of mass transfer coefficient and ration of particle size. The observed change
in the effluent chloride concentration profile is due to sulfate exchange kinetics.
Unlike sodium, calcium, and chloride, Sulfate effluent leakage concentrations are
a strong function of particle size. As shown in Figure 15, a 12.2% decrease in the
effluent equilibrium leakage is observed when the particle sizes are reduced. This change
is due to the desulphonation effect which is directly proportional to the particle size.
4.00E-01
3.00E-01
6.00E-01
:c 5.00E-01
C.
C.
'--'" =o -.. ~
~
..I..-. =QJ
U=o
U-= 2.00E-01
QJ =E~
1.DOE-01
O.ODE+OO
Cation Particle = 0.8 cm Anion Particle = 0.6 cm
Cation Particle = 0.65 cln Anion Particle = 0.55 em
I =- ---
o 100 200 300 400 500
Time (Days)
600 700 800 900 1000
Figure 12. Effect of Resin I>arliclc Size on Sodiunl Concentratioll Profile for a Mixed Bed
Sinlulation Using Divalent fv10del
~v.)
~
J:). c.
c.
~c
.o- ;..
~
J.
;..
C
eJ
~=oU
..... =eJ =e~
6.00E-08
5.00E-08
4.00E-08
3.00E-08
2.00E-08
1.00E-08
O.OOE+OO
Solid line: Cation Particle =0.8 em Anion Particle =0.6 cm
Dashed line: Cation particle =0.65 em Anion Particle = 0.55 em
o 100 200 300 400 500
Time (Days)
600 700 800 900 1000
Figure 13. Effect of Resin particle Size on Calcium Concentration Profile for a Mixed
!Jed Sil11ulation lJsing Divalent Model
~
~
1.00E+01
~..c
e-o.
1.00E+OO
"-"" ....=0....
~
..J...
=QI 1.00E-01
u=0U
....
C
QI = 1.00E-02 e~
1.00E-03
Solid line: Cation Particle == 0.8 cm Anion Particle =0.6 cln
Dashed line: Cation Particle =0.65 cln Anion Particle =0.55 cln
o 100 200 300 400 500
Time (Days)
600 700 800 900 1000
Figure 14. E-II'-Jl"ect ofResI.n l)article Size on C--'hloride Concentrat·ion }>faf-Ie for a Mixed 1
Bed SinllJlation Using Divalellt lTIodel
~
VI
3.70E-03
~ 3.60E-03
~c..
c.
"-'"
Cation Particle = 0.8 em Anion Particle = 0.6 cm
c
.o.. .....
e: ..s...-. =QJ
Cj
Co
U
....- =QJ =e~
3.50E-03
3.40E-03
3.30E-03
3.20E-03
3.10E-03
Cation Particle =0.65 em Anion Particle =0.55 em
~--------------
1
/\
o 100 200 300 400 500
Time (Days)
600 700 800 900 1000
Figure 15. Eflect of I{esin J)articlc Size on Sulfate Concentration Profile for a Mixed Bed
Sinllrlation lJsing J)ivalent Model
~
0\
47
Effects of Resin Ratios
Figures 16 through 18 shows the effect of resin ratios on the predicted effluent
concentration profiles. Resin ratios used were
a) Cation: Anion = 1.5:1,
b) Cation: Anion = 1: 1, and
c) Cation: Anion = 1:1.5.
All the other parameters are maintained at base condition.
As shown in Figure 16, the effluent leakage sodium concentrations are not
affected by change in resin ratios. The effluent concentrations change after 200 days. An
earlier breakthrough by 180 days occurs for a cation/anion ratio of 1.0/1.5 compared to
cation/anion resin ration of 1.5/1.0. Figure 17 shows the chloride effluent concentration
profile for varying resin ratios. There is no change in the effluent leakage concentrations.
Steepness of the breakthrough curves did not change for cation/anion ratio of 1.5/1.0 and
cation/anion ratio of 1.0. Breakthrough was not observed for cation/anion ratio of 1.0/1.5
Figure 18 shows the sulfate effluent leakage concentrations. The effluent leakage
concentrations shows a significant change for different resin ratios. By changing the
cation/anion ratio from 1.5/1.0 to 1.0/1.5, a 55.5% decrease in the effluent sulfate leakage
concentrations is observed. This is due to the desulphonation effect of cation resin.
Conclusions and Recommendations
The divalent model developed here can be used for a wide range of conditions.
Data on selectivity coefficients for divalent exchange as a function of temperature is not
available in the literature and improved predictions are expected when they are
6.00E-01
~
I
".
.. .I
~
I
"
~
" II t1 Cation: Anion = 1.5: 1.0
"
Cation: Anion = 1:1
" " 1/1 -I
I
Cation: Anion = 1.0:1.5 I
I
I
/
/
/
/
,/
~
...-.,l1li' " "" --
2.00E-01
1.00E-01
3.00E-01
5.00E-01
4.00E-01
,..-.....
~
Q.
C.
~
..C
~=E~
c
..o... ~
I-. ..C
~
~
CoU
O.OOE+OO
o 200 400 600 800 1000 1200
Time (Days)
Figure 16. Ef1ect of Resin Ratios 011 SodiuI11 Concentratio11 Profile for a Mixed 13ed
Sin1ulation Using Divalent iv10del
~
00
1.00E+01
~..c
c.
C. 1.00E+00
"-"" =...0.... ..=... =~ 1.00E-01
CJ =:
0U
..... =~= 1.00E-02 e~
1.00E-03
I
•
• • Cation: Anion =0.6:0.4 •
• •
• •
•
• •
• I
I
".
-.........
,
Cation: Anion =0.4: 0.6
o 200 400 600
Time (Days)
800 1000 1200
Figure 17. Effect of Resin Ratios Chloride Concentration Profile for a Mixed Bed
Simulation Using Divalent Model
+::.
\0
,
~---------------
- --- - _.- ...•............
~
,.Qcc..
"'-"'" =o .~ ...... ..=a..... =~
CJ =o
U
...... =~=e~
1.00E-01
1.00E-02
Cation: Anion =1:1
Cation: Anion = 0.6:0.4
I
Cation: Anion = 0.4:0.6
• - ~ I
..
;1 •
200 400 600 800 1000 1200
Time (Days)
Figure 18. Effect of Resin Ratios on Sulfate Concentration Profile for a Mixed Bed
Simulation Using Divalent Model
Vl o
51
incorporated in the model. Desulphonation effects were incorporated into the model and
its predictions agreed with plant data qualitatively. Effect of system parameters on
desulphonation changes sulfate leakage significantly. Sulfate release into the effluent
stream is primarily due to desulphonation. Plant data indicated the presence of
HCO- / C02- in high quantities along with other impurities (Mg+ Cu+) with anion 3 3 ,
equivalent ratios of O.3S0;-:O.5HCO~/ CO;-:O.2CI-. Divalent model does not currently
handle bicorbonate predictions. Actual plant data comparisons can be made when the
divalent model is modified to multicomponent model which can predict the effluent
concentrations of HCO~ / CO;- .
Calcium concentrations are quite lower than expected. Kinetic corrections can be
developed to improve equilibrium relations and its predictions in a multicomponent
exchange and applied to all divalent species.
CHAPTER IV
EFFECT OF PLANT OPERATING PRINCIPLES RESIN
HEEL AND BED CLEANING
Abstract
An MBIE Model for divalent ions is tested for the effects of resin heel (i.e.
uneven distribution of resin in the bed). The model is then extended to address bed
cleaning every three weeks whereby average particle loading after cleaning is used as the
initial loading for the next three weeks. The predictions agree with plant experience.
Introduction
Ion exchange in deep bed polishers is optimum when the cation and anion resins
are homogeneously mixed. The effluent stream will contain minimal quantities of ionic
and organic impurities and near neutral water. However, in practice, it is difficult to
achieve a well mixed bed in service vessels. Thermal degradation of cation resin
exchange sites for sulfate release (discussed in chapter III ) into BWR's is a serious
problem. In addition, the resin is transferred out of the bed for ultrasonic cleaning at
approximately three week intervals. About 10% of the bed, primarily in the form of
cationic resin (due to its weight), classifies at the bottom of the bed. One approach to
avoid this situation has been to replace the cationic heels with an anionic underla:y. The
expected result for this underlay is an increase in organic amines released from the bed.,
52
53
but these amines would decompose in the BWR to amn10nia, organic acids'l nitrogen
oxides and carbon dioxide. All of these products are volatile and would not be expected
to concentrate in the reactor. Reduction in the overall ion exchange performance "vas
expected.
Modeling
An MBIE model for divalent ions is used to evaluate the ionic removal
performance of the bed containing an anionic rich underlay. The base case used 1: 1
cation to anion resin ratios by volume throughout the bed. Sulfate concentration fed to
the column was 3.3 ppb (including 3.0 ppb as a condenser leak). Cation equivalent ratios
of 0.2 Na+: 0.8 Ca+2were used. Chlorine was adjusted to meet electroneutrality criteria.
Water flowrate was 42 gallons per minute per foot square of cross-sectional area..
and the system was operated at an isothermal temperature of 140°F. The bed was 3.35 ill
in diameter and 1.0 m deep. Resin properties, selectivity coefficients, and initial particle
loading are given in APPENDIX F. Diffusion coefficients and pH are a function of
temperature. Mass transfer coefficients are calculated using correlation's by Kataoka or
Carberry depending on flow conditions.
In addition, the model included a sulfate generation term for the cationic resin.
An expression for the kinetic rate constant was used based on data supplied to PP&L by
Fisher and Burke (fig.27). The expression used in the code was
K = 7.5E + 6 x e(-I0278/(T+273.l6»
Where K is a first order reaction rate constant with units of hr-I
, and T is the temperature
of the bed in °C.
Dsing this equation, localized sulfate generation throughout the bed is assumed
constant for an isothermal system. Also, sulfate release is a strong function of flow
54
conditions and water oxygen content. Fisher and Burke's data were generated in beakers
exposed to air. Additional data have been presented in PP&L literature.
To approximate the bed underlay, the same total resin capacity is used, but a 5: 1
anion rich layer is assumed for the bottom 5 cm of the bed (the total anion to cation resin
ratio in the column is 1.07/1.0). Figure 18 through 21 presents the predicted effluent
concentration curves for sodium, calcium, chloride.. and sulfate for these simulations.
Sodium and calcium follow a similar trend and curves become steeper for anionic heels
though not significantly. Chloride breakthrough starts 20 days later for simulation with
anionic heels. Ofparticular note is the reduction in the sulfate equilibrium leakage from
2.2x 10-2 (base case) to 0.7 xl 0-3 ppb. This suggests that using an anionic underlay has
the potential to reduce sulfate leakage ~om the bed significantly when compared to an
ideal mixed bed. The improvement is even greater when compared to a bed operating
with cationic heels. The effluent concentrations were an order of magnitude higher
(1.40E-2 ppb) when operating with a 5 cm cationic heel.
Comparison to Plant Experience
An in-plant test of anion underlays has been performed by PP&L. Ion exchange
units are normally operated with cation-rich heel at the outlets. Each of the seven
condensate polisher vessels was cleaned and an underlay installed while the plant
operated at 100% power. As the number of vessels with underlays increased (they were
brought on-line one at a time), sulfate reactor water gradually dropped from 6-8 ppb to 34ppb.
The reactor water cleanup system (which limits impurity concentrations in reactor
water) processes at 1% of the feed water flow rate. Therefore, the decrease observed in
reactor water sulfate is equivalent to a decrease in the available sulfur in polished effluent
of about 0.03-0.04 ppb as sulfate.
6.00E-01
4.00E-01
3.00E-01 -
I
I
I
I
I
I
I
I
I
~
~
~
~
~
I
5 cm of Cationic Heel
5 cm of Anionic Heel~ /'
-------------------------------.......... /
/
/
/
1:1 Mixed Bed for the Whole Column (Base Case)
~ 5.00E-01 -
~c.
~
~
..o=..=. ...- ..=a..-. =~
CJ
o== ud
2.00E-01
~=e~
1.00E-01-
O.OOE+OO
o 100 200 300 400 500 600 700 800 900 1000
Time (Days)
Figure 19. Effect of Anion Resin Underlay on Sodium Concentration Profile Using MBIE
Model for Divalent Ions.
Vl v,
Solid Line: 1:1 Mixed Bed for the Whole Column (Base Case)
400 500 600 700 800 900 1000
Cationic Hee~
Scm ~ ~.,
A ionic Heel A
Scm n ~~/'
/
100 200 300 "
8.00E-08 -
7.00E-08
~..c
c..
c.. 6.00E-08 ~
...=0...-. 5.00E-08 .=a.....
=~ 4.00E-08
CJ =0U
.... 3.00E-08
=~= 2.00E-08 e~
1.00E-08
O.OOE+OO
0
Time (Days)
Figure 20. Effect of Anion Resin Underlay on Calcium Concentratiol1 Profile Using
MBIE Model for Divalent Ions.
(J,
0'
~ ,.,..-------
5 cm Cationic Hee~" I'
• • I
1:1 Mixed Bed for the Whole Column (Base Case) 'I
~~I
I
I
J5 cm Anionic Heel
I ,~J
1.00E+01
,...-......
~
C.
C. 1.00E+00
'--" =.0-...... ..=a.....
=~= 1.00E-01 -
CJ =0U
...... =~= 1.00E-02 e~
1.00E-03
o 100 200 300 400 500 600 700 800 900 1000
Time (Days)
Figure 21. Effect of Anion Resin Underlay on Chloride Concentration Profile Using
MBIE Model for Divalent Ions.
v..
-.........J
1.60E-02
~ - _ _ .
~
~c.
c. ...........
.=o-~
~... ~=~
CJ =o
U
~=~=e~
1.40E-02
1.20E-02 -
1.00E-02
8.00E-03
6.00E-03
4.00E-03
2.00E-03 -
O.OOE+OO
5 em Cationic Heel
1:1 Mixed Bed for the Whole Column (Base Case)
5 cm Anionic Heel
~---
r
o 100 200 300 400 500
Time (Days)
600 700 800 900 1000
Figure 22. Effect of Anion Resin Underlay on Sulfate Concentration Profile Using MBIE
Model for Divalent Ions.
til
00
59
Sulfur is also released from the cation resin in organic compounds such as resin
fines and soluble materials such as benzene sulfonic acid. This organic sulfur is oxidized
in the BWR to inorganic sulfate. The anion underlays would also act to adsorb some of
these impurities, but the efficiency for adsorption of organics is not likely to be as lligh as
ion exchange.
Calculations at PP&L indicated that inorganic sulfate release from cation-rich
resin heels in the condensate polisher vessels could contribute as much as 4-5 ppb to
reactor water sulfate. Additionally, the sulfate concentration would be strongly
dependent on condensate temperature.
The computer simulation of the divalent model indicates that the inorganic sulfate
release from polishers with well-mixed resins but without underlays would contribute
0.0023 ppb sulfate to feed water, and that the underlays would reduce that by a factor of
5. The reduction in reactor water sulfate observed at PP&L was 3-4 ppb, or about 800/0 of
the calculated contribution from the resin heels. Thus the computer simulation is
consistent with the observations at PP&L, although the actual effluent concentrations are
different. The potential reasons for these differences are
1) Bicarbonate loading: Plant data indicated the presence of HCO~ / CO;- in
high quantities along with other impurities (Mg+,eu+) with anion
equivalent ratios of O.3S0~-:O.5HCO~/ CO;-:O.2CI-. Divalent model
does not currently handle bicarbonate predictions.
2) Organic sulfonates: Decomposition of cation ion exchange resins by the
release of organic sulphonates have been studied (Stahbush, 1987, Fisher,
1987, Cutler, 1988). Plant data indicated the presence of organic
sulphonates but no information is available about organic sulphonate
effect on the predicted concentration levels. Divalent model does not
address this effect.
60
The computer simulation implies that~ if condensate polisher resins are \vellmixed
and heels are avoided, direct inorganic release of sulfate should not be a major
contributor to reactor water sulfate in the B\VR. The contribution of inorganic sulfate to
total reactor water sulfate would be less than 1 ppb. The on-site test results and computer
simulation both support the utility's decision to proceed with modifications to eliminate
cation resin heels and to assure good mixing of resins in the condensate polisher vessels
Bed Cleaning Effects
Figures 22 through 25 shows the effect of bed cleaning every three weeks on the
predicted concentration profiles. Initial particle loading for the simulation is the same as
base case. After three weeks, the bed is cleaned ultrasonically and the resin is loaded into
the column. At this point an average particle loading (based on the condition of the resin
on the twenty-first day) is calculated and taken as the initial particle loading for the next
three weeks.
The effluent concentrations of sodium shows a significant increase for simulation
with bed cleaning every three weeks. After the first three weeks, a 17.1% increase in the
effluent concentrations is observed. It continues to increase to a maximum of 250% at
the end of 550 days. Calcium effluent concentrations at the end of the column run time
increase by more than an order of magnitude for the simulation with bed cleaning
compared to the base case condition. Chloride follows the same trend as sodium but its
increase in effluent concentrations are much higher (98.1% for the first three weeks).
Sulfate effluent concentrations do not change significantly compared to sodium, calcium
and chloride. Initial particle loading for sulfate is higher than any of the other species.
Successive average particle loading of sulfate doesn't change significantly to effect the
effluent concentrations.
6.00E-01 .'------------------------------------tI
Bed Cleaning Every Three Weeks
......-... ..c
~
~
~..,.o=...... ..=a.... =~
CJ =o
U
..... =~=e~
5.00E-01
4.00E-01
3.00E-01
2.00E-01 -
1.00E-01
O.OOE+OO
/
/
/
,/
,/
/
,/
/
/
/
/'
/
,tI
",.,.~ _________ -"" Base Case: No Bed Cleaning
o 100 200 300 400 500
Time (Days)
600 700 800 900 1000
Figure 23. Effect of Bed Cleaning Every Three Weeks 011 Sodium Concentration Profile
0"1
~
6.00E-07
Base Case: No Bed Cleaning
Bed Cleaning Every Three Weeks
J.- --- .."..-----...." ......
1.00E-07
2.00E-07 -
3.00E-07
4.00E-07
...... =~=e~
~ 5.00E-07
C. c..
"--'" ..o=... ...... =... ...... =~
CJ =o
U
O.OOE+OO
o 100 200 300 400 500 600 700 800 900 1000
Time (Days)
Figure 24. Effect of Bed Cleaning Every Three Weeks on Calcium Concentration Profile
0\
to
1.00E+01
------_.11"
~.c
~~
1.00E+00-
~
.o=-= ...... =... ...... =~ 1.00E-01--
CJ =o
U
......
== ~== 1.00E-02
~
~
Bed Cleaning Every Three Weeks
---------
I
I
I
I
/
I
I Base Case: No Bed Cleaning
100 200 300 400 500 600 700 800 900 1000
1.00E-03 -, ,
o
Time (Days)
Figure 25. Effect of Bed Cleaning Every Three Weeks on Chloride Concentration Profile
0\
\jJ
Bed Cleaning Every Three Weeks
800 900 1000
L _
,
500 600 700
,...
I I
Base Case: No Bed Cleaning I I,
100 200 300 400
3.68E-03
3.67E-03
~
,.Q c.. c.. 3.66E-03 ......." =0
..,..... 3.65E-03 =.I..... =~ 3.64E-03
CJ =0U
... 3.63E-03
=~= 3.62E-03 e~
3.61 E-03
3.60E-03
0
Time (Days)
Figure 26. Effect of Bed Cleaning Every Three Weeks on Sulfate Concentration Profile
0'\
~
BIBLIOGRAPHY
Bajpai, R. K., Gupta, A. K. and Gopala Rao, M. (1974). Single particle studies of
binary and ternary cation exchange kinetics. A.I.Ch.E J., 20(5), 989-995.
Bird, R. B., Stewart, W. E., and Lightfoot, E. N. (1960). Transport phenomena.
John Wiley and Sons.
Bokx, P. K. de and Boots,.H. M. J. (1989). The ion exchange equilibrium. J. Phys.
Chern, 93, 8243-8248.
Bokx, P. K. de and Boots, H. M. J. (1990). The compensating-mixture model for
multicomponent systems and its applications to ion exchange. J. Phys. Chern.
94, 6489-6495.
Breslin, R. A. (1991). Condensate polisher resin optimization recommendations
for in-plant tests. Internal report. PP&L.
Calmon, C. (1986). Recent developments in water treatment by ion exchange.
Reactive Polymers, 4, 131-146.
Charles, N. H. (1988). On the existence of ternary interactions in ion exchange.
A.I.Ch.E. J., 34,702-703.
Divekar, S. V., Foutch, G. L., and Haub, C. E. (1987). Mixed bed ion exchange at
concentrations approaching the dissociation of water. Temperature effects.
Ind. En~. Chern. Res., 26(9),1906-1909.
Haub, C. E. and Foutch, G. L. (1986a). Mixed-bed ion exchange at concentrations
approaching the dissociation of water 2. Column model applications. Ind. Eng.
Chern. Fund., 25, 373-381.
Raub, C. E. and Foutch, G. L. .(1986b). Mixed-bed ion exchange at concentrations
approaching the dissociation of water 2. Column model applications. Ind. Eng.
Chern. Fund., 25,381-387.
Haub, C. E. (1984). M.S. Thesis, Oklahoma State University, Stillwater, OK.
65
66
Helfferich, F. G. (1967). Multicomponent ion exchange in fixed beds. Ind. Eng.
Chern. Fund., 6, 362-364.
Helfferich, F. G. (1990). Models and physical Reality in ion-exchange kinetics.
Reactive Polymers, 13, 191-194.
Hogfeldt, E. (1990). A comparison of methods for estimating equilibrium constants
in ion exchange. J. Chern. Soc. Dalton Trans.. 1627-1628.
Holloway, J. H., and James, D. B. (1989). Reduction of corrosion products in the
condensate/feedwater systems at Susquehanna Steam Electric Station. Internal
report, PP&L.
Horst, J., Holl, W. H., and Eberle, S. H. (1990). Application of the surface complex
formation model to the exchange equilibria on the ion exchange resins.
Reactive Polymers, 13, 209-231.
Hwang, Y. L., and F. G. Helfferich. (1987). Generalized model for multispecies ion
exchange kinetics including fast reversible reactions. Reactive Polvmers, 5,
237-253.
Ines, R. T. and Rundberg. R. S. (1987). Determination of selectivity coefficient
distributions by deconvolution of ion exchange isotherms. J. Phys. Chern., 91,
5269-5274.
Kataoka, T. and Yoshida, H. (1988). Kinetics of ion exchange accompanied by
neutralization reaction. A.I.Ch.E. J.. 34, 1020.
Katoaka, T., and Yoshida, H. (1979). Ion exchange equilibria in ternary systems.
J. Chern. En~. o£Japan, ll(4), 328-330.
Kitchener, J. A. (1957). Ion exchange resins. John Wiley and Sons, N.Y.
Kitchener, J. A. (1955). Ion exchange equilibria and kinetics-A critique of the
present state of the theory. Ion exchange and its applications. Society of
chemical industry.
Klien, G., Tondeur, D., and Vermeulen, T. (1967). Multicomponent ion exchange
in fixed beds. Ind. En~.Chem. Fund., 6, 339-351.
Kunin, R. (1960). Elements ofion exchange. Reinhold Publishin2 Corporation,
N.Y.
Lucas, A. D., Zarca, l., and Canizares, P. (1992). Ion-exchange equilibrium of
Ca2+, Mg2+, K+, Na+, and H+ ions on amberlite IR-120: Experimental
67
determination and theoretical prediction of the ternary and quaternary
equilibrium data. Separation Science and Technolo~y, 27(6),823-841.
Morgan, D. J. (1991). Modeling of mixed bed ion exchanger performance.
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Morgan, D. J. (1991). Information on condensate polishing. Personal
communucation, PP&L.
Nachod, F. C., and Schubert, J. (1956). Ion exchange technology. Academic Press
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Noye, J. Computational techniques for differential equations. Elsevier Science
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experimental verification of the Nernst-Planck model for diffusion in an ionexchange
resin. Chern. En~. Sci.. 21, 317-325.
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liquid-phase diffusivity in ion exchange. Ind. En~. Chern. Fund., 24, 423-432.
Yoshida, H., and Kataoka, T.,(1987). Intraparticle ion exchange mass transfer in
ternary system. Ind. En~. Chern, 26, 1179-1184.
Zecchini, E. J. (1990). Solutions to selected problems in multi-component mixed
bed ion exchange modeling. Phd Thesis, 1990, Oklahoma State Universit)T.
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68
APPENDIXES
69
APPENDIX A
ANION FLUX EXPRESSIONS
The anion resin flux expressions will be derived for ternary divalent exchange
(one divalent ion and two univalent ions). The following derivation results from the basic
principles of ion exchange using the Nernst-Planck equation. The necessary assumptions
and conditions will be applied and explained as appropriate.
Raub et al. (1984) developed a binary film diffusion controlled model for
application in mixed bed ion exchange. Zecchini et al (1990) improved the model to
address ternary system (univalent system). The current model incorporates various
modifications to address divalent ions in a ternary system.
Nernst (1904) introduced a simple model where mass transfer is by diffusion
alone and no convective mixing at the surface of the particle. It assumes a static film
surrounding the particle which is separated from the completely mixed bulk liquid by a
sharp boundary. The model is based on linear extrapolation of the limiting concentration
profile at the particle surface, where diffusion alone is effective. In the exchange of ions
of different mobilities, however, an electric field arises and causes electric transference.
This situation led to the development of the Nernst-Planck equation. Assuming the
curvature of the film can be neglected, this expression is:
71
Where ~ is the electrical potential and Z i is the charge or valence on ion i. This applies
to all the species taking part in the exchange process. Pseudo steady state assun1ption
(changes with position are much more important than changes with time) enables the
partial differential equations to be replaced by ordinary derivatives and vice versa.
The flux expressions used in the model are based on the film neutralization
reaction. Interdiffusion within the film is treated as a quasi-stationary diffusion process
across a planar layer or film. This means that the flux across the film adjusts itself
rapidly to the changing boundary conditions. Though, both coions and counterions exist
in the film, a reasonable assumption for avoiding a complex situation is to assume the
flux of coions in the film are negligible. Film neutralization applies to systems with \'ery
low concentrations and small particle size.
There are certain conditions that must be satisfied within the film surrounding the
anionic resin. These are:
~Z.C. =0
L...J 1 1
Jcoions = 0
(electro-neutrality)
(no coion flux into resin),
summation of the fluxes within the film using this expression yields
~L...J Z.J. =0 1 1 (no net current flow)
the film is assumed to be very thin and curvature can be neglected. This assumption
causes a relaxation in the surface condition to include the whole film as;
J coions = 0 (no coion flux)
Applying the above criteria for a six component system with one divalent each in both the
cations and anions yields:
(electroneutrality),
(no net current flow),
(anion exchange; no coion flux),
J =J =J =0 COS (cation exchange; no coion flux)
72
Applying no net coion flux to the Nemst-Planck expression for each of the cation species
(anion exchange) yields an expression for electrical potential ~ as:
d$ RT dCn RT dCh RT dCb
= ----- = ----- = -----
dr Fen dr FCh dr 2FCb dr
Now differentiating the electroneutrality condition with respect to r yields:
(eq. A-I)
dC n + dC h + 2 dC b = dC c + dC 0 + 2 dC s (eq. A-2)
dr dr dr dr dr dr
Now solving for each cation concentration gradient in terms of sodium gradient (Cn) and
inserting into the above equation (eq. A-2) yields:
The left hand side can be written as:
- 1 dC n (C + C h+ 4 Cb)_-d-C -c +dC-0-+2 d-C-s
C n dr n dr dr dr
(eq. A-3)
(eq.A-4)
Now using the condition of electroneutrality (eq. A-I) with the above term (eq. A-4)
gives us an expression in terms of coions as:
(eq. A-5)
eg. A-5 can now be used in eq. A-I to yield an expression for the electrical potential
gradient;
(eq. A-6)
d~ =_ RT (___1 __)(d_Cc +_dC0_+2d_Cs)
dr F C + C + 2C dr dr dr
cos
eq. A-6 allows to remove $ from the flux expressions for chloride, sulfate, and
hydroxide. The fluxes become:
73
(eq. A-7)
(eq. A-8)
(eq. A-9)
(eq. A-IO)
Using the no net current criteria with no coion flux we get:
D (dC c +( C c )( dC c + dC ° + 2 dC s )) +
cdr C c +C o +2C s dr dr dr
D(dC s +( 2C s )(dC c +dC o + 2 dC s ))=O
s dr C c +C o +2C s dr dr dr
collecting the terms and multiplying the above equation by (C c + Co + 2 Cs) yields:
74
eq. A-II can be written as:
-:d=-<DeC 2 ' e +(2D e + 2Do)C oCc +(4D c + 6D s)C sCe + DoC~
dr
+(4D o + 6D s)C oC s + 6D sC;)= 0
(eq. A-II)
(eq. A-I2)
The term in the parentheses is a constant and represents the bulk phase parameters.
eq. A-II can be represented as:
dC 0 = __1 (B dC c + C dC s )
dr A dr dr
where
A = 2D cC e + DeCo + 2D cC s + DoC o + 4D sC s
B = DeC e + DoC e + 2D oC o + 2D oC s + 4D sC s +
C = 2D eCe +2D oCo +2D sCe +2D sCo +I2D sCs
Using the pseudo component technique let's define
Cp = Ch +Cn+Cb = LCi
applying the Nemst-Planck equation for pseudo component equation:
The continuity equation within the film is
dC. _l+UC.+VJ.=O
dt 1 1
when the reactions are restricted to bulk phase neutralization, changes in flux w.r.t. radial
position is negligible i.e.,:
75
dJ j =0
dr
l.e.,
d 2 C __......;;0;""..+
dr 2 dr 2
F d~
+R-(TV·«C -C -C -C )-))=0 poe S dr (eq. A-I3)
The term in the parentheses is the charge balance i.e., equal to zero. eq. A-13 can now
be written as:
d 2 d 2 C
--2...-.t(C 0 + C c + C s)+ 2
P = 0
dr dr
From the charge balance, eq. A-14 can be written as:
. dC P
l.e., --= K I and C p = K I r + K 2
dr
(eq. A-I4)
(eq. A-I5)
a linear profile for coion concentration within the film. Boundary conditions are applied
as:
C P = C· @r = p
C = C 0 @r = p P
o
8
From the boundary condition limitation, constants K1 and K2 are found and replaced as:
76
C p =
C 0 - c p p r + c·p
no coion flux implies that
dC p
dr
=
d$
dr
RT
FC p
from eq. A-I5,
Substituting this in the flux expression for pseudo-component we get;
-J. =D.(dCj -Z.~K)
) 1 dr 1 C
p
)
(eq. A-I6)
C.
let Y i = __I
C p
Differentiating the above equation we get
l.e.,
(eq. A-I7)
dy i -J i = Di(Cp--+(I- Zj)YiKI)
dr
Ii is a constant a shown by earlier applied continuity equation. Thus eq. A-I 7 can be
separated and written in integral form to obtain an expression for the flux.
-J. dy.
_1 -(l-Z.)y.K. =C _1 butC p = KIr + K D. 1 lip dr 2
t
or:
Evaluating within the limits and exponentiating both sides yields:
(K 18 + K 2 ) - 2 = J JD i + (l - Z JK i Y~
K 2 J ./D . + (1 - Z .) K .y ~
1 I I I 1
c·
LHS = (_P_) 2
C 0
P
eq. A-I8 can be written as:
(eq. A-I8)
77
co 0 _ ·C·2
-J.8=(1-Z.)D.(C.-CO
)( pYi Yi p)
1 lip P .2 0 2 Cp -Cp
Remembering the original definition of Yiand converting to fractional concentrations:
or:
- J.8 I
78
The flux expression for any counter ion i is specified by the above expression. This
expression can be used with the static film model rate expression to determine the
effective diffusivity of all the species taking part in the exchanging process.
79
APPENDIXB
PARTICLE RATES
The flux expressions derived in the previous appendixes were developed so that
the particle rates could be determined. The rate of change of resin phase compositions
require that a model for the liquid film surrounding the resin bead be specified. The static
film model will be used in preference to. other available models due to its simple but
accurate form and the low concentrations that this model deals with.
The static film model results in an expression of the form:
(eq. B-1)
The driving force for exchange process is a simple linear relation. However, the nonl-linearity
due to mass transfer coefficient is introduced into the relation as:
,
K. = D ./8 I el (eq. B-2)
Dei is used instead ofD i because in multicomponent exchange the value for the effective
diffusivity is species dependent. The rate of exchange is related to the flux of the species
by:
d<C j>' • --dt~= K. a (C? - C.)= -J.a I S I I I S
The resin phase concentration < Ci >can be represented as:
(eq. B-3)
80
<c. >=y.Q I I'
where Q is the capacity of the resin and Yiis the fraction of species in the resin.
Substituting the above expression in the rate of exchange eq,
,
-dy-i -_ -K-i a (C 0. - C *. )-_ --J ia
dt Q S I I Q S
(eq. B-4)
(eq. B-5)
From eq. B-2 and eq. B-4, an expression for the effective diffusivity can be found as:
D. =_ liD
el (C~ - C:)
This expression can be combined with the relation for Ri as defined by Pan and David
(1978):
R i = ( ~ e~ ) 2/3 = .!S..L
I K i
(eq. B-6)
The right hand portion of eq. B-6 involves the calculation of the non-ionic mass transfer
coefficient which is used in the rate expression. The correlation's of Carberry (1960) and
Kataoka (1973) can be used to determine the non-ionic mass transfer coefficients based
on the particle Reynolds number and species Schmidt number. The final rate expression
reduces to
dy i = K. R . ~C 0 - C')
dt I I Q' I I
where Kiis the non-ionic mass transfer coefficient for species i. Interfacial concentration
C~ is the only unknown variable. The use of selectivity coefficient allows for the
determination of the interfacial concentration.
A relation for the three interfacial concentrations in a ternary system could be
obtained from the selectivity coefficients. For a general reaction
Selectivity coefficients are defined as:
81
K ~ =
( C B
) Z A (C A ) Z 8
(C A)ZB(C B)ZA
(eq. B-7)
The fraction of species on the resin for a ternary anion exchange system is given by:
From the definition of selectivity coefficient, the following expressions result as:
K c Yc C 0 = 0 YoC c
• 2
K S = Y sC 0 Q 0 Y~ C :
• 2
K = Y sC c Q
Y c2 C •s
(eq. B-8)
(eq. B-9)
(eq. B-IO)
The film concentration relation can be applied to determine the interfacial
concentrations (eq. A-12) :
.2 • • • • .2 (DcC c +(2D c + 2D o)C oC c +(4D c + 6D s)C sC c + DoC o
• • .2 +(4D o + 6D s)C oC s + 6D sC s )=
82
This eq represents the anion exchange process between bulk and film taking into account
the basic principles of ion exchange. From eq. B-8 - eq B-IO, C:and C:can be
eliminated and an expression for sulfate interfacial concentration can be found as:
where
A = 6D s
Interfacial concentrations for chloride and hydroxide can be found from the definition of
selectivity coefficients as:
c·o
c·c
The above expressions can now be used with the particle rates to describe the exchange
process.
83
APPENDIXC
COLUMN MATERIAL BALANCES
Material balance equations around the column are required for determining the
effluent concentration profiles. These material balances will use previously determined
rate expressions for individual species. The overall column material balance for species i
is given as:
-Us-a-C+i -aC-i+(-1--E-) aqi -_ 0
E az at E at
where:
(eg. C-l)
Us=superficial velocity, and E = void fraction.
This expression can be simplified by using dimensionless variables in time and distance.
The dimensionless expressions are expressed as:
and,
s= Kj(l- E) Z
Us dp
(eq. C-2)
(eq. C-3)
Ki is the non-ionic mass transfer coefficient for species i, dp is the particle diameter,
Q is the resin capacity and C~ is the total cationic feed concentration. The above
expressions are differentiated with respect to time and distance respectively to yield:
en K jC i m K jC ~ E
- = -- = at d pQ az d pQu s
a~
= 0 and
a~ KjC; E
= at az dpQus
Now using the chain rule the original derivatives are expressed as:
Replacing these into the material balance yields:
This expression is easier to handle. Introducing the fractions in liquid phase and resin
phase as:
x i = C i / C i ,and q i = Qy i
This substitution into the material balance equation yields:
84
85
In the current code, chloride is selected as the reference species. Since all the material
balance is to be solved using same steps in t and ~, expressions for the base species
result as:
This expression is easier to handle. Introducing the fractions in liquid phase and resin
phase where the additional subscript a denotes the anion resin. The corresponding change
in all the species with respect to the base species is:
~=~~)=~~~
a~ a~ e a~ K n d pa ax e '
OY n = ~m C)= ~~!h.oYn
m me m KndpaQame'
OX b = ~~)= ~~~
a~ a~ e a~ K b d pa ax e '
OX s = ~O~ C)= ~~
a~ a~ e a~ K s ax e
= oY s ( mC ) me i7t
86
Replacing into the general material balance equation and introducing the cation (FeR)
and anion (FCA) resin volume fractions within the bed:
AX n + FCR
a~ e
~+ FCR
a~ e
ax C + FCA
a~ e
~+ FCA
a~ e
oy n = 0
aYe
~=o
aYe
oy C = 0
dy e
~=o
aYe
The rate equations that were developed earlier need to be modified to incorporate the
dimensionless variables that have been introduced. This involves changing from t to 1: c
as the basis for the individual species equations.
Changing from t to ~ yields:
oy i = daR.(C ~ _ C ~ ) m pSI C f C f
T T
where ~ is equal to the two thirds power of the diffusivity ratio. It is important to note
that the product of dpas is equal to six. so:
87
By; = 6R(C~ _ et)
m lCf Cf
T T
again changing the basis from ~ to ~x four different equations yields
These represent the rate equations that describe the exchange process. These are
combined with the material balance equations and solved simultaneously to determine the
effluent concentration profiles of each exchanging species. The numerical methods used
to solve them are described in Appendix D.
88
APPENDIXD
NUMERICAL METHODS
The material balance equations outlined in Appendix C for all the exchanging
species are a system of partial differential equations that need to be sol\'ed for finding the
concentration profile history for MBIE column. Constant time and distance steps are
used to calculate the particle loading and bulk phase liquid concentrations down the
column. As seen in Appendix C, rate equation in general form is represented as
Ox fly - =--=Rate=f(y)
a~ in
(eq. D-l)
These system of partial differential equations are solved as ordinary differential equations
keeping one of the parameters as constant while the other is evaluated. This involves the
application of any numerical method using initial value problems.
The application of numerical methods for the divalent model is classified into
two categories based upon its function:
1) Predicting liquid phase concentrations using the distance parameter along the column.
2) Predicting particle loading using the time parameter.
The model is solved for effluent concentrations using backward differentiation
formulas for stiff initial value problems. Backward Euler method of first order (also
called Adams-Moulton method) is used for predicting particle loading.
Backward differentiation formulas are the most common method of solution for
stiff systems. They are linear multi step methods of the form
89
k I a jY n+j = h~ kfn+k
j = 0
where
a k = 1 , a 0 "# 0 and ~ k "# 0
Their order, is equal to step number k, and for orders of one to six they are stiffly
stable. The first order method is the backward Eliler method, and it, together with the
second and third order methods, is absolutely stable in the right half plane not particularly
far from the origin. The higher-order methods do not suffer this problem, but instead are
not absolutely stable in a region of the left half-plane near the imaginary axis.
The backward differentiation formulas are implemented in the same variable order
variable-step manner as the Adam's formulas. A pth order predictor of the form
o
Y n + k =
k - 1
Lj
= 0
•
a j Y n + j
is used to provide the initial estimates for the corrector method described above. The
model cannot use this method for the following reasons.
1) The predictor-corrector loop involves iterative procedure and this changes the
interfacial concentration, which is controlled by kinetics of ion-exchange.
2) An iterative procedure on the interfacial concentration involves the already imposed
Newton Raphson iterative method for finding interfacial concentration and this method
may not converge at all.
Hence as a first estimate a fourth order Runge Kutta method is used in
combination with the backward differentiation predictor in the model to predict the liquid
phase concentrations as a function of the bed depth (and consequently effluent
concentrations).
Table D-I
Coefficients of backward differentiation formulas (Noye~ J.~ 1984).
Order ~k a o a 1 U2 a 3 a 4 a 5 U6
1 1 -1 1
2 2/3 1/3 -4/3 1
3 6/11 -2/11 9/11 -18/11 1
4 12/25 3/25 -16/25 36/25 -48/25 1
5 60/137 -12/137 75/137 -200/137 300/137 -300/137 1
6 60/147 10/147 -72/147 225/147 -400/147 450/147 -360/147 1
90
APPENDIXE
INLET CONDITIONS AND MODEL PARAMETER VALVES
91
The system parameters used for different test conditions are summarized below.
The values are based on the data provided by Pennsylvania Power & Light (PPL).
Base Case Parameters:
Initial Particle loading:
Sodium: 0.01,
Calcium: 0.1,
Chloride: 0.01,
Sulfate: 0.2,
Flow rate =42 gallons per minute,
Temperature = 140°F,
Cation to Anion resin ratio = 1: 1,
Cation Particle Diameter = 0.08 cm,
Anion Particle Diameter = 0.06 cm,
Void fraction ofthe bed = 0.35
Cation resin capacity = 2.1 meq/ml
Anion resin capacity = 1.0 meq/ml
Test Runs:
Temperatures: 120°F and 90°F,
Flow rates: 50 gpm and 57 gpm,
92
Resin ratios: Cation/Anion = 0.4:0.6; Cation/Anion = 0.6:0.4
Particle size: Cation = 0.065 cm ; Anion = 0.055 cm
Mass Transfer Coefficients: Anion mass transfer coefficients were reduced by half in the
program to compare the effluent profiles with the base case results.
Influent concentrations: Sulfate concentration was 3.3 ppb. Sodium feed concentration
was 1: 1 ppb ( So;-13) and cation equivalent ratios of 0.2 Na+ : 0.8 Ca+2 were used.
Chlorine was adjusted to meet electroneutrality criteria. Changes in the system
parameters affected the electroneutrality and consequently changes in the influent
concentrations were done for the affected run. Table E-l shows the numerical values in
the concentrations of the exchanging species which were affected due to the changes in
system parameters.
Table E-l
Values adjusted for Electroneutrality Criteria
Run Type Sodium Calcium Chloride Sulfate pH
(meq/ml) (meq/ml) (meq/ml) (meq/ml)
Base Case O.229E-7 0.917E-7 0.575E-7 0.687E-7 6.50
Temperature at O.229E-7 0.917E-7 0.458E-7 0.687E-7 6.88
32.2° C
Temperature at 0.229E-7 0.917E-7 0.458E-7 0.687E-7 6.64
48.9° C
APPENDIX F
COMPUTER CODE FOR CHAPTER III
93
*
*
*
*
THIS PROGRAM IS USED FOR PREDICTING THE EFFLUENT
CONCENTRATIONS FOR DIVALENT SPECIES.
MULTIVALENT TERNARY ION-EXCHANGE CODE (DIVALENT MODEL)
EMPHASIS ON SULFATE PREDICTIONS INCORPORATING THE
DESULPHONATION OF STRONGLY ACIDIC CATION EXCHANGE
RESIN.
SYSTEM: TERNARY SYSTEM
PARTICIPATING IONS:
CATIONS: SODIUM (N) ANIONS: CHLORIDE(C)
CALCIUM(B) SULFATE (S)
HYDROGEN(H) HYDROXIDE(O)
IMPLICIT INTEGER (I-N), REAL*8 (A-H,O-Z)
REAL*8 KLN, YNC(4,5000),A~C(4,5000),YBC(4,5000),KLS,
1 RATN(4,5000),RATC(4,5000),XSA(4,5000),KLC,KLB,
2 YCA(4,5000),XCA(4,5000),YSA(4,5000),RATB(4,5000),
3 RATS(4,5000),RATEN,RATEC,XBC(4,5000),RATEB, RATES
Correlations-kataoka & carberry:
FI(R,S) = 1.15*VS/(VD*(S**(2./3.))*(R**0.5))
F2(R,S) = 1.85*VS*((VD/(1.-VD))**(1./3.))/
1 (VD*(S**(2./3 .))*(R**(2./3 .)))
* READING THE DATA
*
OPEN(UNIT=9,FILE='s.d',STATUS == 'UNKNOWN')
READ(9,*)KPBK, KPPR, TIME
READ(9,*)YNO, YCO, YBO, YSO
READ(9,*)PDC, PDA, VD
READ(9,*)FR, DIA, CHT
READ(9,*)TAU, XI, FCR, TMP
READ(9,*)DEN, QC, QA~ FAR
READ(9,*)TKSO, TKSC, TKCO, TKCS
READ(9,*)TKNH, TKNB, TKBN, TKBH
READ(9,*)CNF,CBF,CCF,CSF,PH
c---------------------------------------------------------------------
WRITE (6,10)
WRITE (6,11)
WRITE (6,12) YNO,YSO
95
WRITE (6,13) PDC,VD
WRITE (6,14) QC,QA
c-----------------------------------------------------------------------------------------------------------
*
* CALCULATIONS OF DIFFUSION COEFFICIENTS AND NON IONIC MASS
* TRANSFER COEFFICIENTS
*
CP = 1.43123+TMP*(O.000127065*TMP-O.0241537
ALOGKW = 4470.99/(TMP+273.15)-6.0875+0.01706*(TMP+273.15)
DISS = 10**(-ALOGKW)
CHII = ((10.)**(-PH))
COIL = DISS/CHII
CFCAT = CNF + CBF + CHII
CFANI = CCF + CSF + COIL
IF(ABS(CFCAT-CFANI).IJE.(CFCAT/10000))GO TO 446
IF(CFCAT.GT.CFANI) TI-IEN
WRITE(*,444)
444 FORMAT('TOTAL CATIONS IS GREATER THAN TOTAL ANIONS.')
GO TO 448
ELSE
WRITE(*,447)
447 FORMAT(' TOTAL ANIONS IS GREATE~, THAN TOTAL CATIONS.')
ENDIF
448 WRITE(*,445)COII~CHII
445 FORMAT(' COIL = ',E12.5,'CHII =',E12.5)
446 CONTINUE
IF(CFCAT.GE.CFANI) THEN
CF = CFCAT
ELSE
CF=CFANI
ENDIF
WRITE (6,15) CF,FR,DIA,CHT
RTF = (8.931D-10)*(TMP+273.16)
DN = RTF*(23.00498+1.06416*TMP+O.0033196*TMP*TMP)
DO = RTF*(104.74113+3.807544*TMP)
DC = RTF*(39.6493+1.39176*TMP+O.0033196*TMP*TMP)
DR = RTF*(221.7134+5.52964*TMP-O.014445*TMP*TMP)
DS = RTF*(2.079*TMP+35.76)/2.
DB = RTF*(1.575*TMP+23.27)/2.
AREA = 3.1415927*(DIA**2)/4.
VS =FR/AREA
REC = PDC* lOO.*VS*DEN/((l.-VD)*CP) !REYNOLD'S NUMBER
REA = PDA*100.*YS*DEN/((1.-YD)*CP)
SCN == (CP/l OO.)/DEN/DN
SCA == (CP/l OO.)/DEN/DC
SSA == (CP/I OO.)/DEN/DS
SSB==(CP/I00.)/DEN/DB
IF (REC.LT.20.) THEN
KLN == F2(REC,SCN)
KLB == F2(REC,SSB)
ELSE
KLN == F1(REC~SCN)
KLB == Fl(REC,SSB)
ENDIF
IF (REA.LT.20.) THEN
KLC == F2(REA,SCA)
KLS == F2(REA,SSA)
ELSE
KLC == F1(REA~SCA)
KLS == F1(REA,SSA)
ENDIF
**
CALCULATE TOTAL NUMBER OF STEPS IN DISTANCE (NT) DOWN
* COLUMN:SLICES
*
CHTD == KLC*(l.-VD)*CHT/(VS*PDA) !distance dimensionless
NT == CHTD/XI
**
PRINT CALCULATED PARAMETERS
*
WRITE (6,16) DN,DS,DH
WRITE (6,117)DC,DB,DO
WRITE (6,17) CP,DEN~TMP
WRITE (6,18)
WRITE (6, 19)
WRITE (6,20)
WRITE (6,21) TAU,XI,NT
WRITE (6,22) REC~KLN
WRITE (6,88) KLB,KLC
WRITE (6,*)'SULFATE COEFFICIENT: ',KLS
WRITE (6,23) VS
*
-* SET INITIAL RESIN LOADING THROUGHOUT THE ENTIRE COLUMN
96
97
*
MT=NT+ 1
DO 100 M=l,MT
YNC(l,M)=YNO
YBC(l,M)=YBO
YCA(l,M)=YCO
YSA(l,M)=YSO
100 CONTINUE
*
* CALCULATE DIMENSIONLESS PROGRAM TIME LIMIT
* BASED ON INLET CONDITIONS (AT Z=O)
*
TMAXC = QC*3.142*(DIA/2.)**2.*CHT*FCR/(FR*CF*60.)
TMAXA = QA*3.142*(DIA/2.)**2.*CHT*FAR/(FR*CF*60.)
IF(TMAXC.GE.TMAXA) THEN
.TMAX = TMAXC
ELSE
TMAX= TMAXA
ENDIF
TAUMAX = KLC*CF*(TMAX*60.)/(PDA*QA)
DMAX=TMAX/1440.
WRITE(6,*)
WRITE(6,*)
WRITE(6,222)
WRITE(6,223)DMAX
WRITE(6,224)
222 FORMAT(' PROGRAM RUN TIME IS BASED ON TOTAL RESIN CAPACITY')
223 FORMAT(' AND FLOW CONDITIONS. THE PROGRAM WILL RUN
FOR',F12.1)
224 FORMAT(' DAYS OF COLUMN OPERATION FOR THE CURRENT
CONDITIONS.')
*
* PRINT BREAKTHROUGH CURVE HEADINGS
*
IF (KPBK.NE.l) GO TO 50
WRITE (6,24)
WRITE (6,25)
WRITE (6,26)
WRITE (6,27)
WRITE (6,28)
50 CONTINUE
*
* PRINT CONCENTRATION PROFILE HEADINGS
*
T == O.
TAUPR == KLC*CF*(TIME*60.)/(PDA*QA)
IF (KPPR.NE.l) GO TO 60
WRITE (6~30)
WRITE (6,3 1) TIME
WRITE (6,32)
WRITE (6~33)
WRITE (6~34)
60 CONTINUE
*
* INITIALIZE VALUES PRIOR TO ITERATIVE LOOPS
*
J==1
JK == 1
TAUTOT == O.
JFLAG == 0
KK== 1
KPRINT == 1500
*
* DEFINING THE DESULPHONATION TERM(FISHER'S DATA)
* -- CONTEXT TO CODE
*
S1 == (7.5E+6*EXP(-10278.6/(TMP+273.16))*CHTD
1 *3.1415927*(DIA**2.)*2.1)*(VS*PDA)*FCR
1 I(NT*3600. *4.0*FR*KLC*(1.-VD))
*
* TIME STEP LOOP WITHIN WHICH ALL COLUMN CALCULATIONS ARE
* IMPLEMENTED TIME IS INCREMENTED AND OUTLET CONCENTRATION
CHECKED
*
1 CONTINUE
IF (TAUTOT.GT.TAUMAX) GOTO 138
IF (J.EQ.4) THEN
JD == 1
ELSE
JD==J+1
ENDIF
**
SET INLET LIQUID PHASE FRACTIONAL CONCENTRATIONS FOR EACH
* SPECIES IN THE MATRIX
*
COO == COIl
CHO = CHII
XCA(J,1) == CCFICF
XNC(J,I) = CNF/CF
98
99
XBC(J,I) = CBF/CF
XSA(J,I) = CSF/CF
*
* LOOP TO INCREMENT DISTANCE (BED LENGTH) AT A FIXED TIME
*
DO 400 K=I,NT
CNO = XNC(J,K)*CF
CBO = XBC(J,K)*CF
CCO = XCA(J,K)*CF
CSO = XSA(J,K)*CF
*
* CALL ROUTINES TO CALCULATE RN, RB, CNI, CBI(INTERFACIAL
* CONCENTRATIONS
* & COEFFICIENTS)
*
CALL KUMl(DN,DH~DB,CNO,CHO,CBO,TKBH,TKBN,YNC(J,K),YBC(J,K),
1 QC,CNI,CHI,CBI,RN,RB)
XNI = CNI/CF
XBI = CBI/CF
CALL KUM(DC,DO,DS,CCO,COO,CSO,TKSO,TKSC,YCA(J,K),YSA(J,K),
1 QA,CCI,COI,CSI,RC,RS)
XCI = CCI/CF
XSI = CSI/CF
IF (K .EQ. 1) THEN
RATN(J,I) = 6.*RN*(XNC(J,I) - XNI)*KLN*PDA/(KLC*PDC)
RATC(J,I) = 6.*RC*(XCA(J,I)-XCI)
RATS(J,l) = 9.*RS*(XSA(J,1)-XSI)*KLS/KLC
RATB(J,I) = 9.*RB*(XBC(J,1)-XBI)*KLB*PDA/(KLC*PDC)
YNC(JD,I) = YNC(J~I)+TAU*RATN(J,I)*QA/QC
YBC(JD,I) = YBC(J,l)+TAU*RATB(J,I)*QA/QC
YCA(JD,I) = YCA(J,l )+TAU*RATC(J,I)
YSA(JD,l) = YSA(J~I)+TAU*RATS(J,I)
ENDIF
IF «YNC(JD, 1)+YBC(JD.l)).GT.1.0)THEN
CALL CORRECT(Ybc(JD,I),Ync(JD, 1),Ybc(J, 1),Ync(J, 1),TAU,
1 RATEb,RATEn)
RATB(J, 1)=RATEB*QC/QA
RATN(J,I)=RATEN*QCIQA
ENDIF
IF ((YCA(JD, 1)+YSA(JD,1)).GT.l.0)THEN
(:ALL CORRECT(YSA(JD,I),YCA(JD,I),YSA(J,I),YCA(J,I),TAU,
1 RATES,RATEC)
RATS(J,I)=RATES
RATC(J,I)=RATEC
ENDIF
100
*
* IMPLEI\1ENT Il\1PLICIT PORTION OF THE BACKWARD DIFFERENCES
* METHOD FROM TI-lE PRE\lIOUS FUNCTION VALUES. FOR THE FIRST
* THREE STEPS (ALONG THE DISTANCE) USE FOURTH-ORDER RUNGE
* KUTTA METHOD
*
IF (K.LE.3) THEN
FIN == XI*6.*RN*(XNC(J~K)-XNI)*FCR*KLN*PDAI(KLC*PDC)
F2N = XI*6.*RN*((XNC(J,K)+FIN/2.)-XNI)*FCR*KLN*PDAI(KLC*PDC)
F3N = XI*6.*RN*((XNC(J,K)+F2N/2.)-XNI)*FCR*KLN*PDAI(KLC*PDC)
F4N == XI*6.*RN*(XNC(J,K)+F3N-XNI)*FCR*KLN*PDAI(KLC*PDC)
XNC(J,K+l) = XNC(J,K) - (FIN+2.*F2N+2.*F3N+F4N)/6.
FIB == XI*9.*RB*(XBC(J,K)-XBI)*FCR*KLB*PDAI(KLC*PDC)
F2B == XI*9. *RB*((XBC(J,K)+FIB/2.)-XBI)*FCR*KLB*PDAI(KLC*PDC)
F3B = XI*9.*RB*((XBC(J,K)+F2B/2.)-XBI)*FCR*KLB*PDAI(KLC*PDC)
F4B = XI*9.*RB*(XBC(J,K)+F3B-XBI)*FCR*KLB*PDAI(KLC*PDC)
XBC(J,K+l) = XBC(J,K) - (FIB+2.*F2B+2.*F3B+F4B)/6.
FIC = XI*6.*RC*(XCA(J,K)-XCI)*FAR
F2C == XI*6.*RC*((XCA(J,K)+FIC/2.)-XCI)*FAR
F3C = XI*6.*RC*((XCA(J,K)+F2C/2.)-XCI)*FAR
F4C == XI*6.*RC*(XCA(J,K)+F3C-XCI)*FAR
XCA(J,K+I) = XCA(J,K) - (FIC+2.*F2C+2.*F3C+F4C)/6.
FI S == XI*9. *RS*(XSA(J.K)-XSI)*Fi\R*KLS/KLC
F2S = XI*9.*RS*((XSA(J,K)+FIS/2.)-XSI)*FAR*KLS/KLC
F3S = XI*9.*RS*((XSA(J,K)+F2S/2.)-XSI)*FAR*KLS/KLC
F4S = XI*9.*RS*(XSA(J,K)+F3S-XSI)*FAR*KLS/KLC
XSA(J,K+1) == XSA(J,K) - (FIS+2.*F2S+2.*F3S+F4S)/6.+(SI/CF)
ELSE
COEN==3.*XNC(J,K-3)/25. -16.*XNC(J,K-2)/25. +
1 36.*XNC(J,K-I)/25. -48.*XNC(J,K)/25.
XNC(J.K+1) ==-XI* 12.*FCR*RATN(J,K)/25.-COEN
COEB==3.*XBC(J,K-3)/25. -16.*XBC(J,K-2)/25. +
1 36.*XBC(J,K-I )/25. -48.*XBC(J,K)/25.
XBC(J,K+1) ==-XI* 12.*FCR*RATB(J,K)/25.-COEB
COEC=3.*XCA(J,K-3)/25. -16.*XCA(J,K-2)/25. +
1 36.*XCA(J,K-l)/25. -48.*XCA(J,K)/25.
XCA(J,K+1) =- XI*12.*FAR*RATC(J,K)/25.-COEC
COES=3.*XSA(J,K-3)/25. -16.*XSA(J,K-2)/25. +
1 36.*XSA(J,K-l)/25. -48.*XSA(J,K)/25.
XSA(J,K+l) = - XI*12.*FAR*RATS(J,K)/25.-COES+(Sl/CF)
ENDIF
*
* DETERMINE CONCENTRATIONS FOR THE DISTANCE STEP AND
RECALCULATE
* BULK PHASE EQUILIBRIA
101
*
CNO = XNC(J,K+1) * CF
CBO = XBC(J,K+1) * CF
CCO = XCA(J~K+1) * CF
CSO = XSA(J,K+1) * CF
CALL EQB(DISS,CNO~CBO,CCO~CSO,COO,CHO)
*
* DETERMINE RATES AT CONSTANT XI FOR SOLUTIONS OF THE TAU
* MATERIAL BALANCE
*
CALL
KUMl(DN,DH,DB,CNO,CHO~CBO,TKBH,TKBN,YNC(J,K+1),YBC(J,K+1),
1 QC,CNI,CHI,CBI,RN,RB)
XNI = CNI/CF
XBI = CBI/CF
CALL KUM(DC,DO~DS,CCO~COO,CSO,TKSO,TKSC,YCA(J,+Kl),YSA(J,K+1),
1 QA,CCI,COI,CSI~RC,RS)
XCI = CCI/CF
XSI = CSI/CF
RATN(J,K+l) = 6.*RN*((XNC(J,K+1)) - XNI)*KLN*PDN(KLC*PDC)
RATB(J,K+1) = 9.*RB*KLB*((XBC(J,K+1))-XBI)*PDN(KLC*PDC)
RATC(J,K+l) = 6.*RC*((XCA(J,K+1))-XCI)
RATS(J,K+1) = 9.*RS*KLS*((XSA(J,K+l))-XSI)/(KLC)
*
* INTEGRATE Y USING ADAMS BASHFORTH (CALCULATE NEXT PARTICLE
*LOADING FOR THE SAME DISTANCE STEP)
*
YNC(JD,K+l) = YNC(J,K+l) + TAU*RATN(J,K+l)*QNQC
YBC(JD,K+1) = YBC(J,K+l) + TAU*RATB(J,K+l)*QNQC
YCA(JD,K+l) = YCA(J,K+l) + TAU*RATC(J,K+l)
YSA(JD,K+1) = YSA(J,K+1) + TAU*RATS(J,K+l)
*
* CHECK VALUES WITHIN BOUNDS
*
IF ((YNC(JD,K+ l)+YBC(JD,K+ l)).GT.l.O)THEN
CALL CORRECT(Ybc(JD,K+1),Ync(JD,K+1),Ybc(J,K+1),
1 Ync(J,K+1),TAU,RATB(J,K+ l),RATN(J,K+1))
RATB(J,K+ 1)=RATB(J,K+1)*QCIQA
RATN(J,K+1)=RATN(J,K+1)*QCIQA
ENDIF
IF ((YCA(JD,K+l)+YSA(JD,K+l)).GT.l.0) THEN
CALL CORRECT(YSA(JD,K+l),YCA(JD,K+l),YSA(J,K+l),
1 YCA(J,K+1),TAU,RATS(J,K+1),RATC(J,K+1))
ENDIF
400 CONTINUE
*
* PRINT BREAKTHROUGH CURVES
*
IF (KPBK.NE.l) GO TO 450
PN =CNO/l.E-6*23.
PC = CCO/l.E-6*35.5
PS = CSO/1.E-6*48.
PB = CBO/1.E-6*40.
TAUTIM = TAU1-'OT*PDA*QA/(KLC*CF*60.)/1440.
pH = 14.+LOGIO(COO)
IF (KPRINT.NE.1500) GOTO 450
IF(KNC.EQ.2)KNC = 0
77 WRITE(6~139)TAUTIM,PN,PB~PC,PS,PH
139 FORMAT(1x,F11.6,2X,E12.7~2X~E12.7,2X,E12.7,4X,EI2.7,4X,F4.2)
*
102
* STORE EVERY THOUSAND FIVE HUNDREDTH ITERATION TO THE PRINT
* FILE
*
KPRINT = 0
450 CONTINUE
KPRINT = KPRINT+1
JK=J
IF (J.EQ.4) THEN
J = 1
ELSE
J = J+1
ENDIF
*
* END OF LOOP RETURN TO BEGINNING AND STEP IN TIME
*
IF (JFLAG.EQ.l) STOP
TAUTOT=TAUTOT+TAU
GOTO 1
*
* PRINT OUT FORMATS
*
10 FORMAT (' MIXED BED SYSTEM PARAMETERS:')
11 FORMAT (' ')
12 FORMAT (' RESIN REGENERATION',2X,': YNO =',FS.3,
1 ' YSO == '~FS.3)
13 FORMAT (' RESIN PROPERTIES',4X,': PDC ==',F6.4,SX,'VD =',F6.4)
14 FORMAT (' RESIN CONSTANTS',5X,': QC =',F6.4,SX,'QA =',F6.4)
15 FORMAT (' COLUMN PARAMETERS',3X,': CF =',E10.4,' FR =',EI0.5,3X,
1 'DIA =',F6.2~2X.'CHT=',F5.1)
16 FORMAT (' IONIC CONSTAN1~S',5X,': DN =',EIO.4,2X,'DS =',EI0.4,
1 2X,'DH =',E10.4)
117 FORMAT (' IONIC CONSTANTS',5X,': DC =',EI0.4~2X,'DB =',EI0.4~
1 2X,'DO =',EIO.4)
17 FORMAT (' FLUID PROP.',8X,' : CP =',F7.5,4X,' DEN =',F6.3,
1 4X: TEMP =',F6.1)
18 FORMAT (' ')
19 FORMAT (' CALCULATED PARAMETERS :')
20 FORMAT (' ')
21 FORMAT (' INTEGRATION INCREMENTS : TAU =',F7.5,5X,'XI =',F7.5,
1 5X,'NT =',16)
22 FORMAT (' TRANSFER COEFFICIENTS : REC=',EI0.4,' KLN =',EI0.4)
88 FORMAT (' ',25X,' KLB = ',E10.4,2x,'KLC = ',E10.4)
23 FORMAT (' SUPERFICIAL VELOCITY : VS =',F7.3)
24 FORMAT (' ')
25 FORMAT (' BREAKTHROUGH CURVE RESULTS:')
26 FORMAT (' ')
27 FORMAT (6x,' Time',6X:SODIUM',6x,'CALCIUM',8X,'CHLORIDE',
1 8X,'SULFATE',6x,'pI-l')
28 FORMAT (' ',6X,'Days'.7x,'ppb',11X,'ppb',11X,'ppb',13x,'ppb')
29 FORMAT (' ',4(4X,E8.3),5X.F4.2)
30 FORMAT (' ')
31 FORMAT (' CONCENTRATION PROFILES AFTER ',F5.0,' MINUTES')
32 FORMAT (' ')
33 FORMAT (' ',5X,'Z',7X~'XNC',7X,'YNC',
1 7X,'YCA')
34 FORMAT (' ')
35 FORMAT (' ',6(2X,E8.3))
138 STOP
END
*
* THE SULFATE SUBROUTINE-> (CALCULATION OF ANIONIC
INTERFACIAL
* CONCENTRATIONS)
*
SVBROUTINE KUM(DC,DO,DS,CCO,COO,CSO,TKSO,TKSC,YC,YS,
QA,CCI,COI,CSI,RC,RS)
IMPLICIT REAL*8(A-H, O-Z)
EPSILON = 1.0E-14
EPN = 2.13.
S = DC*CCO**2+((2.*DC)+(2.*DO))*COO*CCO
1 +((4.*DC)+(6.*DS))*CSO*CCO+DO*COO**2.
1 +((4.*DO)+(6.*DS))*COO*CSO+6.*DS*CSO**2.
YO = 1. - YC - YS
YO=ABS(YO)
A =6.*DS
103
B = ((4.*DC)+(6.*DS))*YC*SQRT(TKSC)
1 +((4.*DO)+(6.*DS))*YO*SQRT(TKSO)/SQRT(YS * QA)
E = (DC*TKSC*YC**2.+((2.*DC)+(2.*DO))*YO*YC*SQRT(TKSO*TKSC)
1 +DO*TKSO*YO**2.)/(YS*QA)
XO=E
X = XO -((A*XO**4.) + (B*XO**3.) + (E*XO**2.) - S)/
1 ((4.*A*XO**3) + (3.*B*XO**2) + 2.*E*XO)
DO WHILE ((ABS(X-XO)/X).GT.EPSILON)
XO=X
X = XO -((A*XO**4.) + (B*XO**3.) + (E*XO**2.) - S)I
1 ((4.*A*XO**3.) + (3.*B*XO**2.) + 2.*E*XO)
END DO
IF(X.LT.O.O) THEN
X =0.0
ENDIF
CSI = X**2.
COl = YO*SQRT((TKSO * CSI)/(YS*QA))
IF(COI.LT.O.O)COI=O.O
CCI = YC*SQRT(TKSC*CSI/(YS*QA))
IF(CCI.LT.O.O)CCI=O.O
CTI = CSI + COl + eCI
CTO = CSO + COO + ceo
C-------------------------------------------------------------
C CALCULATE TERNARY DIFFUSIVITIES
C--------------------------------------------------------------
IF(ABS(CSO - CSI).GE.(CSO/l 00000.)) GO TO 52
DESS = 0.0
GOTO 53
52 DESS = 3.*(CTI/CTO*CSI/CSO-l.)/
1 (l.+CTI/CTO)/(l.-CSI/CSO)
53 IF(ABS(CCO - CCI).GE.(CCO/IOOOOO.)) GOTO 59
DEC = 0.0
GOTO 61
59 DEC = 2.*(CTI/CTO*CCI/CCO-l )/(1.+CTI/CTO)/(1.-CCI/CCO)
61 CONTINUE
RS = (ABS(DESS))**EPN
RC = (ABS(DEC))**EPN
RETURN
END
* ------------------------------------------------------------
* INTERFACIAL CONCENTRATIONS FOR CATIONS: 1 DIVALENT AND 2
MONOVALENT
* BASED SIMILAR TO SULFATE SUBROUTINE :
* ------------------------------------------------------------
SUBROUTINE KUMl(DN~DH~DB~CNO~CHO,CBO,TKBH,TKBN,YN,YB,
104
QC,CNI.CHI,CBI.RN,RB)
IMPLICIT REAL*8 (A-I-I. O-Z)
EPSILON == 1.0E-14
EPN = 2./3.
S = DN*CNO**2+((2.*DN)+(2.*DH))*CHO*CNO
+((4.*DN)+(6.*DB»*CBO*CNO+DH*CHO**2.
1 +((4.*DH)+(6.*DB»)*CHO*CBO+6.*DB*CBO**2.
YH = 1. - YN - YB
A = 6.*DB
B = ((4.*DN)+(6.*DB))*YN*SQRT(TKBN)
1 +((4.*DH)+(6.*DB)*YH*SQRT(TKBH)/SQRT(YB * QC)
E = (DN*TKBN*YN**2.+((2.*DN)+(2.*DH»*YH*YN*SQRT(TKBH*TKBN)
1 +DH*TKBH*YH**2.)/(YB*QC)
XO=E
X = XO -((A*XO**4.) + (B*XO**3.) + (E*XO**2.) - S)I
1 ((4.*A*XO**3.) + (3.*B*XO**2.) + 2.*E*XO)
DO WHILE ((ABS(X-XO)/X).GT.EPSILON)
XO=X
X = XO -((A*XO**4.) + (B*XO**3.) + (E*XO**2.) - S)/
1 ((4.*A*XO**3.) + (3.*B*XO**2.) + 2.*E*XO)
END DO
IF(X.LT.O.O) THEN
X=O.O
ENDIF
CBI =X**2.
CHI = YH*SQRT((TKBI-I * CBI)/(YB*QC»
IF(CHI.LT.O.O)CHI=O.O
CNI = YN*SQRT(TKBN*CBI/(YB*QC»
IF(CNI.LT.O.O)CNI=O.O
CTI = CBI + CHI + CNI
CTO = CBO + CHO + CNO
C-------------------------------------------------------------
C CALCULATE TERNARY DIFFUSIVITIES
C--------------------------------------------------------------
IF(ABS(CBO - CBI).GE.(CBO/I00000.» GO TO 52
DEBB = 0.0
GOTO 53
52 DEBB = 2.*(CTI/CTO*CBI/CBO-l.)/
1 (l.+CTI/CTO)/(l.-CBI/CBO)
53 IF(ABS(CNO - CNI).GE.(CNO/l 00000.) GOTO 59
DEN = 0.0
GOTO 61
59 DEN = 1.*(CTI/CTO*CNI/CNO-l)/(1.+CTI/CTO)/(1.-CNI/CNO)
61 CONTINUE
RB = (ABS(DEBB»**EPN
105
**
*
*
*
*
*
RN = (ABS(DEN))**EPN
RETURN
END
SUBROUTINE E.QB(DISS~CNO,CBO,CCO,CSO,COO,CHO)
Subroutine to calculate bulk phase concentrations
based on amine equilibriul11
IMPLICIT REAL*8 (A-I-I,O-Z)
V1=(CNO+CBO-CCO-CSO)**2.+4.*DISS
COO=(CNO+CBO-CCO-CSO+(V1 **0.5))/2.
CHO=DISS/COO
RETURN
END
SUBROUTINE CORRECT(YSA~YCA,YSAOLD,YCAOLD,TAU,
1 RATES,RATEC)
Subroutine to correct tIle bulk concentration when the
calculated loading exceeds 1.0 011 the resin
IMPLICIT REAL*8 (A-H~O-Z)
YYY=YSA+YCA-1.0
IF (ysa.GE.yca) TI-IEN
IF (YSA.GT.1.0) THEN
YSA=0.999999
YCA=0.0000005
GOTO 120
ELSE
YCA=YCA-YYY
IF (YCA.LE.O.O) THEN
YCA=0.0000005
YSA=0.999999
ENDIF
ENDIF
ELSE
IF (YCA.GT.l.0) THEN
YCA=0.999999
YSA=0.0000005
GOTO 120
ELSE
YSA=YSA-YYY
IF (YSA.LE.O.O) THEN
YSA=O.0000005
YCA=O.999999
ENDIF
ENDIF
106
ENDIF
120 RATES =(YSA-YSAOLD)/TAU
RATEC =(YCA-YCAOLD)/TAU
RETURN
END
107
VITA
Sudhir K. Pondugula
Candidate for the Degree of
Master of Science
Thesis: MIXED BED ION EXCHANGE MODELING FOR DIVALENT
IONS IN A TERNARY SYSTEM
Major Field: Chemical Engineering
Biographical:
Personal Data: Born in Vijayawada, India, March 01, 1970, the son of Rajyalakshmi
and Ramaiah Venkata Pondugula.
Education: Graduated from Kendriya Vidyalaya Central School, Visakhapatnam, AP,
India, in May 1988; received Bachelor of Technology Degree in Chemical
Engineering from Andhra University in May 1992; completed requirements for
the Master of Science degree at Oklahoma State University in May, 1995.
Professional Experience: Employed as a research assistant, School of Chemical
Engineering, Oklahoma State University, September 1992 to May 1994.